Chemistry-
General
Easy
Question
In homogeneous catalytic reactions, there are three alternative paths A,B and C (shown in the figure) which one of the following indicates the relative ease with which the reaction can take place?
![](data:image/png;base64,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)
The correct answer is: ![C greater than B greater than A](data:image/png;base64,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)
Related Questions to study
Chemistry-
In a spontaneous adsorption process
In a spontaneous adsorption process
Chemistry-General
Chemistry-
Graph between log
and log P is a straight line at angle 0 45 with intercept OA as shown Hence ,
at a pressure of 2 atm is
![](data:image/png;base64,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)
Graph between log
and log P is a straight line at angle 0 45 with intercept OA as shown Hence ,
at a pressure of 2 atm is
![](data:image/png;base64,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)
Chemistry-General
Maths-
If
and
then
If
and
then
Maths-General
Maths-
Assertion : For
the volume of the parallel piped formed by vectors
and
is maximum (The vectors form a right-handed system)
Reason: The volume of the parallel piped having three coterminous edges
and ![stack c with ‾ on top](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAZCAYAAADjRwSLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAY00gKyAAAAGxJREFUeNpjYICA/zjwKBgFOAAPEHcB8VMg/gXE64BYEF3BOSBuBWI+IGYD4hIg9kFW1AHEk/BZwwTEr9GNRgemQHyYkIO9oI7EC4yB+AYx3r8A9RkL1HcFQGyNrkgWiA8C8R8gvgTEySSFMAC4kxWWWazxUwAAAHd0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+YzwvbWk+PG1pPiYjeDIwM0U7PC9taT48L21vdmVyPjwvbWF0aD6siPvzAAAAAElFTkSuQmCC)
For such questions, we should know the formula of a parallelepiped. We should also know how to take a scalar product.
Assertion : For
the volume of the parallel piped formed by vectors
and
is maximum (The vectors form a right-handed system)
Reason: The volume of the parallel piped having three coterminous edges
and ![stack c with ‾ on top](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAZCAYAAADjRwSLAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAY00gKyAAAAGxJREFUeNpjYICA/zjwKBgFOAAPEHcB8VMg/gXE64BYEF3BOSBuBWI+IGYD4hIg9kFW1AHEk/BZwwTEr9GNRgemQHyYkIO9oI7EC4yB+AYx3r8A9RkL1HcFQGyNrkgWiA8C8R8gvgTEySSFMAC4kxWWWazxUwAAAHd0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+YzwvbWk+PG1pPiYjeDIwM0U7PC9taT48L21vdmVyPjwvbWF0aD6siPvzAAAAAElFTkSuQmCC)
Maths-General
For such questions, we should know the formula of a parallelepiped. We should also know how to take a scalar product.
Maths-
Assertion (A): Let
. If
such that
is collinear with
and
is perpendicular to
is possible, then
.
Reason (R): If
and
are non-zero, non-collinear vectors, then
can be expressed as
where
is collinear with
and
is perpendicular to ![stack a with rightwards arrow on top](data:image/png;base64,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)
Assertion (A): Let
. If
such that
is collinear with
and
is perpendicular to
is possible, then
.
Reason (R): If
and
are non-zero, non-collinear vectors, then
can be expressed as
where
is collinear with
and
is perpendicular to ![stack a with rightwards arrow on top](data:image/png;base64,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)
Maths-General
Maths-
Statement
If
are distinct non-negative numbers and the vectors â
and
are coplanar then
is arithmetic mean of
and
.
Statement -2: Parallel vectors have proportional direction ratios.
Statement
If
are distinct non-negative numbers and the vectors â
and
are coplanar then
is arithmetic mean of
and
.
Statement -2: Parallel vectors have proportional direction ratios.
Maths-General
Maths-
If
and
is a vector satisfying
.
Assertion
can be expressed in terms of
and
.
Reason ![left parenthesis R right parenthesis colon r with ‾ on top equals 1 over 7 left parenthesis 7 i plus 5 j minus 9 k plus a with ‾ on top cross times b with ‾ on top right parenthesis](data:image/png;base64,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)
If
and
is a vector satisfying
.
Assertion
can be expressed in terms of
and
.
Reason ![left parenthesis R right parenthesis colon r with ‾ on top equals 1 over 7 left parenthesis 7 i plus 5 j minus 9 k plus a with ‾ on top cross times b with ‾ on top right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN0AAAAoCAYAAAB6m/+wAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAc1CXO0QAABOxJREFUeNrtm1Fk1VEcx/+umT1k9DAzPVySJJORJEliZpKZuNJDD4lJJpnoYWaSMTM99JZJkhkzkySRmSSJZKaHRHpKJnpIcl2X9Tv6Xf079/zO//zvPed//7t9P/zY/d//Ped/fud8z++c3/8sigAAjbItGAAAAAAAAFgDAwDagv1kU2QbcAUmdZAND8nG0BEAtGZGBABAdABAdAAAiA4AiA4AANEBANEBIHKFbDblb2b5d+0sukb8AkCiPg6RvW6w4Ff8+3YUXTN+AcCqD/XFgPCjMg/UL2RvyJ6S9cS+P0z2coeILe0RId0v2wlm4hdZIXA7ktrj+xkUJ7nfy1z+CtneDOvPAy7tMupjgAeXiX1R/VnFGbI57dpLLrydsPlFp0S2IPhvs8XL4xDPMET2nuwID7oOsktkH8h6M6g/D6RpV50+lIDGhZtHyRa1a+fI7mvXrrbhvsfmlzi97NSujMSUh0TQWyGqlQwTshpDSxlOMlmRpl11+nhGdkK4eZrsunbtJtk17doxsjVHZ6kyb5Bd5s4r8+e8YfNLnMeWpfl0iraFEt10AP9Whesq6r2z1K8i4gOy04FEV+DxuUVW4VVa0XL/JFva72rtmuT6vvI4XifrM9xbp48fZJ1CwctkI7HP3cISopPLcXHWMu8P5y17AJf9U+gZ0OaXGmrimLJ8v8wzYitFl+YZXPkkbCeKvM8x1d/Ff58KGOmekN0h280CdGm7SVxJgqu16xNPKLX6bgvRr04fVUvBH1m5aoYa5lmsJNxbcXSMKvPsDlheVhO+L3JiqSOhrXsCiK7CnaiSWhNkuzw9gytqDHzmZEqB7QyPj4qh/n5eERwNuLw8z0KI4xpV4yJzEVytXQe1a92G4GPUh22pUNUii2255SK6gmEmDMF2g5ZGdC8SZu2ktjYbyTs42kzx6uOAcE+oZzjJy6ky2zInF34ZfPCaheer70ys8zJO76OiY71KaM8dBSf1bZer6KRl1FFuSHxdOicU2GmpzFZmFHBQhlxeljjK+GprswmDIR5gpr3EepQdXRz9dR+oKHQvcCJFT9+rv3+mqCeN6KS+NeU2jPpQFR0XwrWepXwuzBxSZS5l5hXJLwWOLAOe29rsJFLOgb9V5L8l1D/Pe+BQovumfT5uSOr4Wl5Kfp0Q9vh1+pBS42pDOmb48QPDveOWKKiXeWmHiE7yy6gQVZptazOi6+dNvUsfhmRG2z/q9UsTmQ+/fIn+fW2jBv9KSsG5JlJUuy4aotlmZM5e1ulDegm8KmxC1wwbSNPL8e0UZeYRyS9LBodHHtrqOrhWefKrJTCGWXCm5NSjQP5e4/pqy+89PMhHEnywm5effQH8oiLsXfaJWo0tOmwBGn1lsMqJlMFY+1ct48J4eERtdPXzYd8j8wvfY1pjpGNgJmdJZeYVk1+2ePAkEaqtJe7wKtehEhhHMn6GQd7TVHmvshSZzxea6u9n0YZ4rkn2xxSXvxX5f11SGwMjsX7YsNQjHpNs5wPPzSRjdvKB514eFP8zPTl4Bqs+1CY37VGuuYz3DL4jxoLDfY34pdUUOHExEYFW5wXG4Ia/UcDHecm8cSH6k8X8GeF/AEHOsJ2XBAB4Jum8JADAIy7nJQEAHkk6LwkA8IjLeUkAgCdcz0sCADzhel4SAOAJ1/OSAABPuJ6XBCAovwHm96FWkK2boQAAAbl0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+KDwvbW8+PG1pPlI8L21pPjxtbz4pPC9tbz48bW8+OjwvbW8+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPnI8L21pPjxtaT4mI3gyMDNFOzwvbWk+PC9tb3Zlcj48bW8+PTwvbW8+PG1mcmFjPjxtbj4xPC9tbj48bW4+NzwvbW4+PC9tZnJhYz48bW8+KDwvbW8+PG1uPjc8L21uPjxtaT5pPC9taT48bW8+KzwvbW8+PG1uPjU8L21uPjxtaT5qPC9taT48bW8+LTwvbW8+PG1uPjk8L21uPjxtaT5rPC9taT48bW8+KzwvbW8+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPmE8L21pPjxtaT4mI3gyMDNFOzwvbWk+PC9tb3Zlcj48bW8+JiN4RDc7PC9tbz48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+YjwvbWk+PG1pPiYjeDIwM0U7PC9taT48L21vdmVyPjxtbz4pPC9tbz48L21hdGg+0mMygAAAAABJRU5ErkJggg==)
Maths-General
Maths-
If
are non-zero vectors such that
then
Assertion
: Least value of
is ![2 square root of 2 minus 1](data:image/png;base64,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)
Reason (R): The expression
is least when magnitude of
is ![square root of 2 t a n invisible function application open parentheses fraction numerator pi over denominator 8 end fraction close parentheses end root](data:image/png;base64,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)
If
are non-zero vectors such that
then
Assertion
: Least value of
is ![2 square root of 2 minus 1](data:image/png;base64,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)
Reason (R): The expression
is least when magnitude of
is ![square root of 2 t a n invisible function application open parentheses fraction numerator pi over denominator 8 end fraction close parentheses end root](data:image/png;base64,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)
Maths-General
Maths-
Statement- 1: If
and
and
, then there exist real numbers
,
such that
![alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma d](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAAWCAYAAADZylKgAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAAtpJREFUeNrtWE9kHFEcHisiqkLEqorIpSpyKhUR1UOoqlW1Qg49RESo6KmirKqqqFJVVatCRNWqKlGjh4peImJVbhGrqkL1UBFVonqoqmX6Pb6p1583k9nNvNlt+j4+OzszO+/37/2+36znpYun4FHPoa2wBG6DIy4U2eMqGMSwDp50YWqfnfIRHHahaB+0u6Y4zXOa5+A0j/gB5lqw7iz4DvwJVsH+Q6J5B47nCbDWAsPvgI+oDcqBB+DzQ6ApqcSzCL5IwZigQcM3xbmJBpJi2z4r8ewFK2wLFVFVFQYgxG3wJjgP7vI3a+Bxi07fIHVU9xFu5cN9cAf8BfpgjwX7lEZtRVzLcxcMaTaVwW+M20vwMViSP+wE34IFHq/xRoUBQ4Uusz+X6KRqJQ+b2D2NJGWZFaUwCK5QX+ISouy+C3bTr+vgRUv2LYKT4lwHC2eM33OM7TSPu1nggebbH9wSVXiKQffYHs6K+7e1zIdQC3y3mBS1Zh8/AwZ8KOb+e6zIrNrXoEEXFsA5EedSjG9/4bNBBNfB83ywjhwnBYmuBEkJEtAEuWaeVb/HYJju/9pgqzqIfSFUtznD43HwVYI4G+N5mltMYgbcMDxkhFtQYhRctVSJUWvOR+yG4QifbAv9LKfDPDWmV3Sf9aS+TURoQYWZl7jM8VJijtvThtNRa6oe/sRwvkBRzzopx9j2VewuiGtq5zxL6tu4wYElilGVo6iOMq/JQaFmcfoqR4j6Klusafd/aNFIXIsolCKHFQmVqCueQaA/cazrYdYWeW3FUP0+hekcv/fx3LRFp306O6q9s/gRuyfEFievDvp4Tev3NpOywPUkjoDv2cbCwnnNcb1getAA+9qmeB+ZMkwUX8BLTEydzhctv1ztcY0dzvYbtC0O/ezhdfowk9GL4Jt92puv+TBG37r+tf/YOpsYtVtp6673HyAt0Xa2poipFF4Cs8Kk9k9IU/gNCI7PnKz60+0AAAD9dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPiYjeDNCMTs8L21pPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5iPC9taT48bW8+JiN4MjE5Mjs8L21vPjwvbW92ZXI+PG1vPis8L21vPjxtaT4mI3gzQjI7PC9taT48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+YzwvbWk+PG1vPiYjeDIxOTI7PC9tbz48L21vdmVyPjxtbz4rPC9tbz48bWk+JiN4M0IzOzwvbWk+PG1pPmQ8L21pPjwvbWF0aD7aEMwVAAAAAElFTkSuQmCC)
Statement- 2:
are four vectors in a 3 - dimensional space. If
are non-coplanar, then there exist real numbers
such that ![stack a with rightwards arrow on top equals alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma stack d with rightwards arrow on top](data:image/png;base64,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)
Statement- 1: If
and
and
, then there exist real numbers
,
such that
![alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma d](data:image/png;base64,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)
Statement- 2:
are four vectors in a 3 - dimensional space. If
are non-coplanar, then there exist real numbers
such that ![stack a with rightwards arrow on top equals alpha stack b with rightwards arrow on top plus beta stack c with rightwards arrow on top plus gamma stack d with rightwards arrow on top](data:image/png;base64,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)
Maths-General
Maths-
Statement-
:If
are non-collinear points. Then every point
in the plane of
, can be expressed in the form ![open parentheses fraction numerator k x subscript 1 end subscript plus l x subscript 2 end subscript plus m x subscript 3 end subscript over denominator k plus l plus m end fraction comma fraction numerator k y subscript 1 end subscript plus l y subscript 2 end subscript plus m y subscript 3 end subscript over denominator k plus l plus m end fraction close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ0AAAArCAYAAABikN2XAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAdoyL+RwAABeVJREFUeNrtXVGEXUcYHrEiYoVVEasirFh5iOhbRUSUilgR+xZ5iIhlVZ/6UKIqoiJEVB5q5aVWxIolIg8RESIioqJErKiKJaoPVRFWVNVa4XZ+9z9xdu45986cmTnzn8z38bM799y53z/z3f/M/Ofc8ytVja+1LSgAAHLFTxwHrHBY24q2MYwbAGQL+v6/1HZk1IHbtf2h7TOLTv/TtqWDg9FV3hhb8G0b+zkejA876KK2axad7eUo1DV0lTfGFnxTblMu1r24U9s7bZ9adDSrbVmAQz3H41Pw7mUirtSakKyFLmtgUts/HB8G8L22JcuOLmg7V9r73NA2Yxwzp+1yzWpmLtFklHlL5Fjw28UR/o22v0tjO6HtqrY1nsjvWvbFRxOL2k5WvO8bbZcSa0ESt6YaiOkD9X2+6oXfVT8JaoNbHKm38d9f1Bz3gp0vcFaFvSrjKpSCt1SOt1g0z7Wd4i/fHt5XUsR/wsKg9t3a1g3usX3x0cQZbVeMNsqhrWr7JLEWJHFrqoGYPhzS9spsnNb21qGTVU6S3NX2+ZDjjnFUJHyp7VHiZd9qxfZLEsdV/vwJo/0vbT/XtE+26IuPJmb4C2GeVc8L0IIkbk01ENsHWvHsU8YZ6ablmynbTFnnZyySUXio+pdtVgJEvJ6FjeItlWPBb7tje0xfVEBNEJffSv/THvk1r0xSa0EKNx8NhPbBxE2OEx9A+8+vLN9MZ5HHvHRatDie9lQb2g4kTjAVvKVyrOPn2h7TF19NlL+oV5mrFC1I4OargZg+zHGc+IB7ajCRWQcSxnX++8cRwYb2QrfZgVNDjpvmZdRKRKGUebtyLM4O9GX8RfUv14XmWMfPpd3VFxrvowEEZauJp9qm2F6r6nskUmlhFLcuaMDFB9e5p63v/XLDW1VzSaUClNGdN5bDhyqOm+L9LS2pxjmxU7dcXuI+exGFYvJ25VgsB+nW2hcROFbxc2l39UXxHvXPAEHDVhN0pjrBS93TwrRgw026Bmx9aDL348rIe7rcGXfHWJVQYuZXIyG3k6NSWbTH1ehLujGFYvJuypGwHoHjnZrVnk17U19oztcCBA0bTRRbJ9q+vAw8t75acOUmUQOuPrjO/UAOzWXA1yqSK5T8esTtW9mZqpvElnmZE0ooqiFvH46UZHwSmZ9Le1NfKMAsmMmtgNzLmigwy3N8IkLQ8OXrwk2aBlx9aDr3G21NUKyzRQpM8n52SnUbxd72dMufS2J+JlQLttwka8DGB5+57yFouIESdPcqltxdxQ7Vv1NwvsXPpC3UQaFasOEmXQO249t07hE0HFcY93mwPzast/Q5+/kLJ1ELNtyka8B1fJvMPYKGYwTf9xEGDPrZwHPBWyhoQNbciwoaLnfzgV8YX+gs80D1f9eAsc5DA75zL3KlAQCA7KCDoAEAAIIGAAAIGgAAdC1o9GBZma2AYHnNPVYaAABgewIAAIIGAAAIGkCXsMz6mMVQIGggaAAIGkDjoPFeONm2y+ehXN9g4JiBDrLHRlcGp+3yeSjXtxlU15eecj0GHWSNMWU8uYtqJ0wIJetbPi9mub4ctnX0RLBd0EH2OqCnfW16Rij9Dv+YULI2JSBDTqhZujFU3z4lFwHoIDWI36ankdNj0M8KFYttCchQYqkq3Riib9+Si7kDOkiLeWWUUaDnBS4JFYttCchQYqkq3Riib9+Si7kDOkiLZXNhMc3LJGlwLQFZTGCM0o0+fYcquZgroIP0oHzGwJPLKFN8UJhYXEtA+p4FhpVu9Ok7VMnFXAEdpAVtBV9VvfCtx4TEgksJyBBiqSt/59t3iJKLOQM6SAtKXVQmZOmSyjuHfVwbsC33F0osdeXvfPv2LbeXO6CDdKBk7L9qSIlPyuouCBKLbbm/UGKpK3/n27dvub3cAR2kAyVnfxh2ACViqNr0ASFisS33F/PzYvbr2p4roIM0oLuB6VLw+KgDadlHZejHoFUAyBZUI5gujhy2fQPto65h3AAgW1CaojLh/D8TVqaJEGE7XAAAAlh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZlbmNlZCBzZXBhcmF0b3JzPSJ8Ij48bXJvdz48bWZyYWM+PG1yb3c+PG1pPms8L21pPjxtc3ViPjxtaT54PC9taT48bW4+MTwvbW4+PC9tc3ViPjxtbz4rPC9tbz48bWk+bDwvbWk+PG1zdWI+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdWI+PG1vPis8L21vPjxtaT5tPC9taT48bXN1Yj48bWk+eDwvbWk+PG1uPjM8L21uPjwvbXN1Yj48L21yb3c+PG1yb3c+PG1pPms8L21pPjxtbz4rPC9tbz48bWk+bDwvbWk+PG1vPis8L21vPjxtaT5tPC9taT48L21yb3c+PC9tZnJhYz48bW8+LDwvbW8+PG1mcmFjPjxtcm93PjxtaT5rPC9taT48bXN1Yj48bWk+eTwvbWk+PG1uPjE8L21uPjwvbXN1Yj48bW8+KzwvbW8+PG1pPmw8L21pPjxtc3ViPjxtaT55PC9taT48bW4+MjwvbW4+PC9tc3ViPjxtbz4rPC9tbz48bWk+bTwvbWk+PG1zdWI+PG1pPnk8L21pPjxtbj4zPC9tbj48L21zdWI+PC9tcm93Pjxtcm93PjxtaT5rPC9taT48bW8+KzwvbW8+PG1pPmw8L21pPjxtbz4rPC9tbz48bWk+bTwvbWk+PC9tcm93PjwvbWZyYWM+PC9tcm93PjwvbWZlbmNlZD48L21hdGg+xIFQnQAAAABJRU5ErkJggg==)
Statement-
:The condition for coplanarity of four points
is that there exists scalars
not all zeros such that
where
.
Statement-
:If
are non-collinear points. Then every point
in the plane of
, can be expressed in the form ![open parentheses fraction numerator k x subscript 1 end subscript plus l x subscript 2 end subscript plus m x subscript 3 end subscript over denominator k plus l plus m end fraction comma fraction numerator k y subscript 1 end subscript plus l y subscript 2 end subscript plus m y subscript 3 end subscript over denominator k plus l plus m end fraction close parentheses](data:image/png;base64,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)
Statement-
:The condition for coplanarity of four points
is that there exists scalars
not all zeros such that
where
.
Maths-General
Maths-
Assertion (A): The number of vectors of unit length and perpendicular to both the vectors.
and
is zero Reason
(R):
and
are two non-zero and non-parallel vectors it is true that
is perpendicular to the plane containing
and ![stack b with ‾ on top](data:image/png;base64,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)
Assertion (A): The number of vectors of unit length and perpendicular to both the vectors.
and
is zero Reason
(R):
and
are two non-zero and non-parallel vectors it is true that
is perpendicular to the plane containing
and ![stack b with ‾ on top](data:image/png;base64,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)
Maths-General
Maths-
The value of
for which the straight lines
and
are coplanar is
For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.
The value of
for which the straight lines
and
are coplanar is
Maths-General
For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.
Maths-
The position vector of the centre of the circle ![vertical line r with rightwards arrow on top vertical line equals 5 comma r with rightwards arrow on top times left parenthesis i with ˆ on top plus j with ˆ on top plus k with ˆ on top right parenthesis equals 3 square root of 3](data:image/png;base64,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)
The position vector of the centre of the circle ![vertical line r with rightwards arrow on top vertical line equals 5 comma r with rightwards arrow on top times left parenthesis i with ˆ on top plus j with ˆ on top plus k with ˆ on top right parenthesis equals 3 square root of 3](data:image/png;base64,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)
Maths-General
Maths-
Let
where
are three noncoplanar vectors. If
is perpendicular to
, then minimum value of ![x squared plus y squared](data:image/png;base64,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)
Let
where
are three noncoplanar vectors. If
is perpendicular to
, then minimum value of ![x squared plus y squared](data:image/png;base64,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)
Maths-General
Chemistry-
Which of the following represents Westrosol?
Which of the following represents Westrosol?
Chemistry-General