Maths-
General
Easy
Question
The value of
for which the straight lines
and
are coplanar is
- -1
- 1
- 2
Hint:
We are given equation of two straight lines. We are given that the lines are coplanar. Coplanar lines means line containing in the same plane. We have to find the value of p for which the lines are coplanar.
The correct answer is: ![negative 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAANCAYAAABCZ/VdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAHRJREFUeNpjYCAfWAPxGiD+BMS/gPgCEEczUAkcBOJIIOaB8rWA+ChUjCZAHogvMdAQ/KCVwZbQoKE64ADik9CIxgD/icC4gCAQbwBiN2q7WAlqsAq1DdYA4tlAzEVtg8WBeBUQs9AiArdAXU4TQE7EUw8AAPHyHrtKzRGZAAAAU3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4tPC9tbz48bW4+MjwvbW4+PC9tYXRoPttGRG0AAAAASUVORK5CYII=)
The given equation of the lines are as follows:
![r with rightwards arrow on top equals left parenthesis 2 i with hat on top space plus space 9 j with hat on top space plus space 13 k with hat on top right parenthesis space plus space t left parenthesis i with hat on top space plus space 2 j with hat on top space plus 3 k with hat on top right parenthesis
r with rightwards arrow on top equals left parenthesis negative 3 i with hat on top space plus space 7 j with hat on top space plus space p k with hat on top right parenthesis space plus space s left parenthesis negative i with hat on top space plus space 2 j space with hat on top plus 3 k with hat on top right parenthesis](data:image/png;base64,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)
We have to find the value of p such that the lines are coplanar.
The conditions for coplanarity is as follows:
If two lines are given by
![table attributes columnalign left end attributes row cell r with rightwards arrow on top equals a with rightwards arrow on top subscript 1 plus beta subscript 1 stack b subscript 1 with rightwards arrow on top end cell row cell r with rightwards arrow on top equals stack a subscript 2 with rightwards arrow on top plus beta subscript 2 stack b subscript 2 with rightwards arrow on top end cell row blank row blank end table](data:image/png;base64,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)
Here, the first term represents the position vector of a point through which line is passing. Second term is for the vector parallel to the given line.
The condition for coplanarity is as follows:
![open parentheses a with rightwards arrow on top subscript 1 minus stack a subscript 2 with rightwards arrow on top close parentheses. left parenthesis stack b subscript 1 with rightwards arrow on top space cross times space stack b subscript 2 with rightwards arrow on top right parenthesis space equals space 0](data:image/png;base64,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)
If we see it is an scalar triple product. So, the scalar triple product should be zero.
![W e space w i l l space f i n d space stack a subscript 1 with rightwards arrow on top minus stack a subscript 2 with rightwards arrow on top space f i r s t. space L e t space u s space d e n o t e space i t space b y space a with rightwards arrow on top
a with rightwards arrow on top space equals space stack space a subscript 1 with rightwards arrow on top space minus space stack a subscript 2 with rightwards arrow on top space
space space space space equals space 2 i with hat on top space plus space 9 j with hat on top space plus space 13 k with hat on top space minus left parenthesis negative 3 i with hat on top plus space 7 j with dot on top space plus space p k with hat on top right parenthesis
space space space space equals left parenthesis 2 plus 3 right parenthesis i with hat on top space plus left parenthesis 9 minus 7 right parenthesis j with hat on top space plus left parenthesis 13 minus p right parenthesis k with hat on top
space space space space equals 5 i with hat on top space plus 2 j with hat on top plus left parenthesis 13 space minus space p right parenthesis k with hat on 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We will solve the scalar triple product now.
![a with rightwards arrow on top. left parenthesis stack b subscript 1 with rightwards arrow on top cross times stack b subscript 2 with rightwards arrow on top right parenthesis space equals open vertical bar table row 5 2 cell 13 minus p end cell row 1 2 3 row cell negative 1 end cell 2 cell negative 3 end cell end table close vertical bar
space space space space space space space space space space space space space space space space space 0 equals 5 left parenthesis negative 6 minus 6 right parenthesis minus 2 left square bracket left parenthesis negative 3 right parenthesis space minus left parenthesis negative 3 right parenthesis right square bracket plus left parenthesis 13 minus p right parenthesis left square bracket 2 minus left parenthesis negative 2 right parenthesis right square bracket
space space space space space space space space space space space space space space space space space 0 equals negative 60 space plus space 0 space plus left parenthesis 13 space minus p right parenthesis 4
space space space space space space space space space space space space space space space space space 0 equals negative 60 space plus 52 space minus 4 p
space space space space space space space space space space space space space space space space space 0 space equals space minus 8 space minus 4 p
R e a r r a n g e space t h e space e q u a t i o n
space space space space space minus 8 space minus 4 p space equals 0
A d d space 8 space t o space b o t h space t h e space s i d e s
space space space space space space space space space space space space minus 4 p space equals 8
space space space space space space space space space space space space space space space space space space p space equals negative 2
space space space space space space space space space space space space space space space space space space space 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)
So, the value of p for which the lines are coplanar is -2.
For such questions, we should know the condition for two lines to be coplanar. We should also know about the scalar triple product.
Related Questions to study
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
Chemistry-
Which of the following sequences would yield -nitro chlorobenzene (Z) from benzene?
Which of the following sequences would yield -nitro chlorobenzene (Z) from benzene?
Chemistry-General
Chemistry-
For the preparation of chloroethane
For the preparation of chloroethane
Chemistry-General
Chemistry-
Which of the following statements is wrong about the reaction?
Which of the following statements is wrong about the reaction?
Chemistry-General
Chemistry-
In the following reaction, the final product can be prepared by two paths (I) and (II).
Which of the following statements is correct?
![](data:image/png;base64,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)
In the following reaction, the final product can be prepared by two paths (I) and (II).
Which of the following statements is correct?
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)
Chemistry-General
Chemistry-
The final product (X) in the following reaction is:
![](data:image/png;base64,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)
The final product (X) in the following reaction is:
![](data:image/png;base64,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)
Chemistry-General
Chemistry-
Ethylmercaptan is prepared by the reaction of the following, followed by hydrolysis
Ethylmercaptan is prepared by the reaction of the following, followed by hydrolysis
Chemistry-General
Maths-
Two adjacent sides of a parallelogram
are given by
and
. The side
is rotated by an acute angle
in the plane of parallelogram so that
becomes AD’. If
makes a right angle with the side AB then the cosine of angle
is given by
Two adjacent sides of a parallelogram
are given by
and
. The side
is rotated by an acute angle
in the plane of parallelogram so that
becomes AD’. If
makes a right angle with the side AB then the cosine of angle
is given by
Maths-General
Maths-
If
then ![stack b with ‾ on top equals](data:image/png;base64,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)
If
then ![stack b with ‾ on top equals](data:image/png;base64,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)
Maths-General
Maths-
If
are non coplanar vectors then the roots of equation ![open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell left square bracket b with not stretchy bar on top cross times c with not stretchy bar on top c with not stretchy bar on top cross times a with not stretchy bar on top a with not stretchy bar on top cross times b with not stretchy bar on top end cell end table close square brackets x squared](data:image/png;base64,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)
![Error converting from MathML to accessible text.](data:image/png;base64,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)
![plus left square bracket b with not stretchy bar on top minus c with not stretchy bar on top c with not stretchy bar on top minus a with not stretchy bar on top a with not stretchy bar on top minus b with not stretchy bar on top right square bracket plus 1 equals 0](data:image/png;base64,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)
If
are non coplanar vectors then the roots of equation ![open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell left square bracket b with not stretchy bar on top cross times c with not stretchy bar on top c with not stretchy bar on top cross times a with not stretchy bar on top a with not stretchy bar on top cross times b with not stretchy bar on top end cell end table close square brackets x squared](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAK0AAAAaCAYAAADFYNyOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAAxBJREFUeNrtWzFoVEEQ/RwSQhBBJEgIQRARsUgjIiGFTYoQRK5NeaSzCiFgcYQQRBALi2BjFUQkcIQUIdiISBA7CSGVCJZBQrogEiRgZrh38Fn2zt3Z/ff/HvPgwd2/z9zczNvZmf1clsXBPwsV6aPSeVXBKZLTkwpVkZy2VLSKqmmrU6X/Er8Sb6Us2lh9lvbhaVTaGvEJcV8rbboDTWqLLZZ/ZypaRUqifUjcU9EqUhHtGHramypaRQqivU3chXD19EBRedGyUD8Qr4Qa7tX8/8GkpxgshObV1MoC8YXlvmf4rAMW7J0Yq6HbfXyGdqj5HTjEyKtNM3x8dT33vkF83aNAWgtlqGjrxE3N8cAhRl5tmpklvsLrGeKnIvuObvetEpvENeKvrH2m9rlbAw00Qd/POrhMfEk8ytpPTbaJVwW/3dVOiL81xOYY33FAvCEUga+tEL8leXXVzMesfZTF/l8rQ7Qt4k/iUyS8hpX0v1VqC5qrYHmLeY5GfYi4THwkEKyPHam/PAGv52LTQhWTQGJL6rc0ry6aWcSimyx6wut23w/iXeMai+DUwWY+eC6BzNDIr0fY/iR2fP2dR/LzeEucE/gbYksS55C89tLMNHELC2C+DNHWMGGaGPb4cU1sFy6B5O87EbYCsez4+Mvb6ZRxbU/YHoTa8o1zaF5tmuGHBDvEEex038poDx4gmCamPBpsn2DeJ36JUGVD7Pj4ax4Z8evfkY6ffG35+B0jr6ZmRnGUlRcpt2Lv+i1aLu8blutLxJUCtq05DEuhkNrx9ffEsjXuC30OsSVpa0LyampmCPEet9yziROFvomWe8KGcY0dPHSYMiUDwj3i9wiildiR+HuELbWDFfRzEkhtSfwOyatEW32ttNto2GfwfhzXGoJAugb0ABP/JQwGi6g6vvCxI/WXn/S8wVbOved7bJESSGxJ/ZbmNQnR8nnhY/zAcwihnhWLCQwg51j5CyXbcal0LVTGYcSsXgFbvRArr5UUrcIfoxW1Vaa2CjN8lqNCkYRoFYpKiVb/4KdIQk8X4vw5nFiMEBwAAAMtdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mZW5jZWQgY2xvc2U9Il0iIG9wZW49IlsiIHNlcGFyYXRvcnM9InwiPjxtdGFibGUgY29sdW1uYWxpZ249ImxlZnQgbGVmdCBsZWZ0IiBjb2x1bW5zcGFjaW5nPSIxZW0iPjxtdHI+PG10ZD48bXJvdz48bW8+WzwvbW8+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPmI8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeEFGOzwvbW8+PC9tb3Zlcj48bW8+JiN4RDc7PC9tbz48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+YzwvbWk+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4QUY7PC9tbz48L21vdmVyPjwvbXJvdz48bW8+JiN4MjAwNTsmI3gyMDA1OyYjeDIwMDU7JiN4MjAwNTs8L21vPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5jPC9taT48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3hBRjs8L21vPjwvbW92ZXI+PG1vPiYjeEQ3OzwvbW8+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPmE8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeEFGOzwvbW8+PC9tb3Zlcj48bW8+JiN4MjAwNTsmI3gyMDA1OyYjeDIwMDU7JiN4MjAwNTs8L21vPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5hPC9taT48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3hBRjs8L21vPjwvbW92ZXI+PG1vPiYjeEQ3OzwvbW8+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPmI8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeEFGOzwvbW8+PC9tb3Zlcj48L210ZD48L210cj48L210YWJsZT48L21mZW5jZWQ+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tYXRoPhF7zUcAAAAASUVORK5CYII=)
![Error converting from MathML to accessible text.](data:image/png;base64,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)
![plus left square bracket b with not stretchy bar on top minus c with not stretchy bar on top c with not stretchy bar on top minus a with not stretchy bar on top a with not stretchy bar on top minus b with not stretchy bar on top right square bracket plus 1 equals 0](data:image/png;base64,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)
Maths-General
Maths-
If the squares of the lengths of the tangents from a point P to the circles
,
and
are in A.P then
are in
If the squares of the lengths of the tangents from a point P to the circles
,
and
are in A.P then
are in
Maths-General
Chemistry-
In the following redox reaction,
Number of moles of
reduced by 1 mole of
is
In the following redox reaction,
Number of moles of
reduced by 1 mole of
is
Chemistry-General
Maths-
The vector
equals
The vector
equals
Maths-General