Question
The vectors
are equal in length and pair wise make equal angles. If
, then ![c with not stretchy bar on top equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABoAAAATCAYAAACORR0GAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAASM53j1gAAAHpJREFUeNpjYICA/1jwKBgFo2CQAx4g7gLip0D8C4jXAbEgLSw5B8StQMwHxGxAXALEPljU/icC4wQdQDyJ1kHGBMSvaRFM6MAUiA+ToJ7soPOCRjzNgTEQ36BX0r4ATXEs0FRXAMTWtLBIFogPAvEfIL4ExMlDsiQAAFy0JoXYQWz7AAAAkHRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5jPC9taT48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3hBRjs8L21vPjwvbW92ZXI+PG1vPj08L21vPjwvbWF0aD6pOx6qAAAAAElFTkSuQmCC)
Hint:
We are given three vectors of same length. The angle between the pairs of the vector is same too. We are given the two vectors. We have to find the remaining vector. We will assume the variables for the remaining vector. We will use it for all the given conditions. Then, we will find the values of the variable hence the vector.
The correct answer is: ![left parenthesis 1 comma 0 comma 1 right parenthesis](data:image/png;base64,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)
The given vectors are
.
![a with rightwards arrow on top equals i with hat on top plus j with hat on top space
b with rightwards arrow on top equals j with hat on top plus k with hat on top](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAzCAYAAAAjKt6MAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAY00gKyAAAArBJREFUeNrtWUEoREEYniRtklIkObjIQXuV5KScFLk6SFKSo4uDNsnFQQ5uknCQkiTJRZKTXCTlosRF2pSDJKHW/+d/9Xp53syb/f99uztffe2+efvmm/nnn5l98ymVDNSXiIYVxoFf9FnMGrFRDdwA3gD76XODyotJwwrt1Kh1X6Oq6fqG7heDhvUoPQBHQu5j+b3lqOVdA6NXwxQMm/viGqvAW2CnKhNMAnP/8BvYxtyGd2BFUjUwI+6AHcwNbAVeJ1mDa42wRY5bANNmDpgFfgKvgC0CHZsFTjMHwkjjELgMrKOg7AAHNRoVxSjo6NgGQltjiH7sxyawTyAjcGdqZg6EtsYpsCtQdiYwNSpoNefMukoNjdCtBb+/aY6OTSM7aRA4F8suE43nwHU38FJgWgzR7sQZCCONR2DKd50B7goEAhfnMeZALJu8gs8DV2hK4LqwBTwSCMRejAXZNBD7phoztHNkKDuyhttaHLwEMjGRGg0l8B7VSFtnWQOn+SJwqlwDMAz8oO1/QTk4ODg4ODgUAlJnllIGbWwdCV9DyqDV0imEryFl0OZFh8vXkDJo86bDsUZImMCSOtaNtLmfNJ3ShYQRWwhto7oljNhCaBvXjWeT20WSuTnOfqFJioe3aAI/qd8THjRFmgQ6xmkC++tGxyvSxtyh/wz4kGcCL2lEM+kmsFd3ir73RD1w+8cfjFrgq0BGcJrAWHcaeKDzqhBmxKYEAqFj0MbNOq9f5xSMSIQZsWienjBPDSOD1jAjvH6h97mm80CYSYp+QIY5IzhNYH/d6G9MRD2AJulooKyK9l/uXcPIoDUMRLDuY/Xr8odijxaVXrpuprJRgYXS2KA1CETQYMbd8OK/wUWzd4CCgWcPV4rf/PXAaQL/VXea1r2UShCcQaucQZtMg/YHAeP6RRBJszMAAAGBdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPmE8L21pPjxtbz4mI3gyMTkyOzwvbW8+PC9tb3Zlcj48bW8+PTwvbW8+PG1vdmVyPjxtaT5pPC9taT48bW8+XjwvbW8+PC9tb3Zlcj48bW8+KzwvbW8+PG1vdmVyPjxtaT5qPC9taT48bW8+XjwvbW8+PC9tb3Zlcj48bW8+JiN4QTA7PC9tbz48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjxtb3Zlcj48bWk+YjwvbWk+PG1vPiYjeDIxOTI7PC9tbz48L21vdmVyPjxtbz49PC9tbz48bW92ZXI+PG1pPmo8L21pPjxtbz5ePC9tbz48L21vdmVyPjxtbz4rPC9tbz48bW92ZXI+PG1pPms8L21pPjxtbz5ePC9tbz48L21vdmVyPjwvbWF0aD6zOFz1AAAAAElFTkSuQmCC)
![L e t space c with space rightwards arrow on top equals x i with hat on top plus y j with hat on top space plus z k with hat on top](data:image/png;base64,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)
All the three vectors are of equal lengths.
...(1)
![open vertical bar a with rightwards arrow on top close vertical bar equals square root of 1 plus 1 end root
space space space space space space equals square root of 2](data:image/png;base64,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)
So, the length of all the vectors will be √2
Let the angle between each pair from the given vectors be A.
Let's write the dot product of each pair.
![a with rightwards arrow on top. b with rightwards arrow on top equals open vertical bar a with rightwards arrow on top close vertical bar open vertical bar b with rightwards arrow on top close vertical bar cos A](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIQAAAAXCAYAAADKtudKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAWNPAnzwAAAxtJREFUeNrtWDFoFEEUXY4QLA4hRZAQRBCRIEFswhFS2FiJHCGNXCESBAsLERFEwiEitiJiIyJiIYEjBBFJIxKCWAgSJEgQwcJC5EgXJEgIjH/kHQzDn939w252cjcPHsnO3v6Zt/v2z/+bJOXjBbGeHFyogrSqJOI/nhG/ExsBPDCfOKogrQNniGsQ7eIe8WSfGMJHa8wQxlvzgzg1IBnCpTUaYp9qiJAM0fc1xEEoCMt+YCow4/Z1QbjfN9qn6BtIQxRZEO4QaxUbosiiTxWkNURD3Ci7IDxB3Ag8Q0iLPlWQ1tAMcZG4Sxwqs4aYJS4OSA0h1RqSIUZg5nfQ4YROf/eIXbjnC/GYYKK7xAXE+E38S1wljlVkCIkeqSGkWl1xZohruP4n8ZJ1/gJxE+vXf5tMjOOYe8fYFtPwlNgiXiY+SfvhW+JjOEjfzE6Wgyx0kJJvGzEe5niTVA76GEKiR2oIqVYuzhniFtZUQ13zyjjfwByTOJ7E8bQV57PDKBymcV80jiAeixZEmnhJPC8whK7gT1ljh4nbFWQIqR6pIaRauThLxOsp2paQIeyM8Zopbkdy3KshmOeoMbZOnOB+vMo4b02wZdSwMBuHKjKEVI/EED5auTjbMJEL+vywNTbMzKEzzEe8BFlb+i1r7AG6sswWSv//R/BgGngIXIp6X8GWIdUjMYSPVuVRaLrO7zJjdXRRm45PBBPIBjbOEt9wk2wxxc66wBAtVPE2bhLbFWQIqR6JIXy0Kscai8gQJu44dH5IednY9vMXUl4PbexheaGLt3lm8RsVdRlSPRJD+GhVju8iWTVEk9keljO2bjuDXCU+Srlmkaut7qMdqWGf1dXuSo4038MyCq1zOB7H2HxF3yF89OQd99GqHO2ibjXnsE4d57lxfgpdQK94PY3jmZR5rljb2RiMWs+4hjXMAirzNt6ubkabZorsws36Ru2h559NykfaPizVk3fcR6srvm49PxlxmkxX8Q1v/VfHPOYn+RUrS3WYTsXGOLRkYjQJH5IvgKMFZYiy1xkRwI2OhoiGiA8sIiIV/wChjU5/E3SXhAAAAbJ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+YTwvbWk+PG1vPiYjeDIxOTI7PC9tbz48L21vdmVyPjxtbz4uPC9tbz48bW92ZXIgYWNjZW50PSJ0cnVlIj48bWk+YjwvbWk+PG1vPiYjeDIxOTI7PC9tbz48L21vdmVyPjxtbz49PC9tbz48bWZlbmNlZCBjbG9zZT0ifCIgb3Blbj0ifCI+PG1vdmVyIGFjY2VudD0idHJ1ZSI+PG1pPmE8L21pPjxtbz4mI3gyMTkyOzwvbW8+PC9tb3Zlcj48L21mZW5jZWQ+PG1mZW5jZWQgY2xvc2U9InwiIG9wZW49InwiPjxtb3ZlciBhY2NlbnQ9InRydWUiPjxtaT5iPC9taT48bW8+JiN4MjE5Mjs8L21vPjwvbW92ZXI+PC9tZmVuY2VkPjxtaT5jb3M8L21pPjxtaT5BPC9taT48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjwvbWF0aD4y/aZtAAAAAElFTkSuQmCC)
![open parentheses i with hat on top plus j with hat on top close parentheses. open parentheses j with hat on top plus k with hat on top close parentheses equals open vertical bar a with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar cos A
space 0 space plus space 1 space plus space 0 space equals space open vertical bar a with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar cos A
R e a r r a n g e
open vertical bar a with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar cos A space equals space 1 space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right 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)
The next pair will be
![b with rightwards arrow on top. c with rightwards arrow on top equals open vertical bar b with rightwards arrow on top close vertical bar open vertical bar c with rightwards arrow on top close vertical bar cos A](data:image/png;base64,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)
![open parentheses j with hat on top plus k with hat on top close parentheses times open parentheses x i with hat on top plus y j with hat on top plus z k with hat on top close parentheses equals open vertical bar b with rightwards arrow on top close vertical bar open vertical bar c with rightwards arrow on top close vertical bar cos A
y space plus space z space equals space open vertical bar a with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar cos A space space space space space space space space space space space space space space... left parenthesis space u sin g space 1 right parenthesis
y space plus space z space equals space 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis u sin g space 2 right parenthesis space space space space space space space space space space](data:image/png;base64,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)
![c with rightwards arrow on top. a with rightwards arrow on top equals open vertical bar c with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar cos A](data:image/png;base64,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)
![open parentheses x i with hat on top plus y j with hat on top plus z k with hat on top close parentheses. open parentheses i with hat on top plus j with hat on top close parentheses equals open vertical bar c with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar cos A
x space plus space y space plus space 0 space equals space open vertical bar a with rightwards arrow on top close vertical bar open vertical bar a with rightwards arrow on top close vertical bar cos A space space space space space space space... left parenthesis u sin g space 1 right parenthesis
x space plus space y space equals space 1 space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis u sin g space 2 right parenthesis](data:image/png;base64,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)
Now we will solve the equation
y + z = 1 ...(3)
x + y = 1 ...(4)
Subtracting (4) from (3)
z - x = 0
x = z
Now, we know that length of all vectors is √2
![open vertical bar c with rightwards arrow on top close vertical bar equals square root of x squared plus y squared plus z squared end root
square root of 2 space equals square root of x squared plus y squared plus space z squared end root
space S q u a r e space b o t h space t h e space s i d e s space a n d space r e a r r a n g e
x squared space plus space y squared space plus space z squared space equals space 2
w e space k n o w space x space equals space z
2 z squared space plus space y squared space equals space 2](data:image/png;base64,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)
We will rearrange equation (3) and substitute in the above equation.
y + z = 1
y = 1 - z
![2 z squared plus y squared equals 2
2 z squared plus left parenthesis 1 space minus space z right parenthesis squared space equals space 2 2 z squared space plus space 1 space minus space 2 z space plus space z squared space equals space 2
3 z squared space minus 2 z space minus 1 space equals space 0
F a c t o r i s e
3 z squared space minus 3 z space plus space z space minus space 1 space equals space 0
3 z left parenthesis z space minus space 1 right parenthesis space plus space 1 left parenthesis z space minus space 1 right parenthesis space equals space 0
left parenthesis 3 z space plus space 1 right parenthesis left parenthesis z space minus space 1 right parenthesis space equals space 0
z space equals space minus 1 third space o r space z space equals space 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If we see the options, we don't have the value of z component as fraction. So, we will just focus on the value of z = 1
y = 1 - z
y = 1 - 1
y = 0
x + y = 1
x + 0 = 1
x = 1
![c with rightwards arrow on top equals i with hat on top plus 0 j with overparenthesis on top plus k with hat on top](data:image/png;base64,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)
The solution is (1,0,1).
For such questions, concept of scalar product is important. When we take a dot product of two vectors, we get a scalar value. This is called as scalar product.
Related Questions to study
The figure shows elliptical orbit of a planet m about the sun s . the shaded area SCD is twice, the Saded area SAB. If t1 is the time tor the planet to move trom C' and U and t2 is the time to move from A to B then
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)
The figure shows elliptical orbit of a planet m about the sun s . the shaded area SCD is twice, the Saded area SAB. If t1 is the time tor the planet to move trom C' and U and t2 is the time to move from A to B then
![](data:image/png;base64,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)
A Particle of mass
is at rest at t=0. The force exerting on it in
-direction is
. Which one of the following graph is of speed ![V left parenthesis t right parenthesis rightwards arrow t](data:image/png;base64,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)
A Particle of mass
is at rest at t=0. The force exerting on it in
-direction is
. Which one of the following graph is of speed ![V left parenthesis t right parenthesis rightwards arrow t](data:image/png;base64,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)
As shown in figure a block of mass
is aftachod with a cart. If the coefficient of static friction between the surface of cart and block is
than what would be accelcration
of cart to prevent the falling of block ?
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)
As shown in figure a block of mass
is aftachod with a cart. If the coefficient of static friction between the surface of cart and block is
than what would be accelcration
of cart to prevent the falling of block ?
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)
If the vectors
and
make an abtuse angle for any
, then
belangs to
If the vectors
and
make an abtuse angle for any
, then
belangs to
A geostationary satellite is orbiting the earth at a height of 5R above that of surface of the earth. R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of earth is hr.
A geostationary satellite is orbiting the earth at a height of 5R above that of surface of the earth. R being the radius of the earth. The time period of another satellite in hours at a height of 2R from the surface of earth is hr.
The most common minerals of phosphorus are
The most common minerals of phosphorus are
The time period T of the moon of planet Mars(Mm) is related to its orbital radius R as (G = Gravitational constant)
The time period T of the moon of planet Mars(Mm) is related to its orbital radius R as (G = Gravitational constant)
A mass of 6 kg is suspended by a rope of lengih 2 m form the ceiling . A force of 50 N in the horizonlal direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ?
Neglect mass of the rope:
![](data:image/png;base64,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)
A mass of 6 kg is suspended by a rope of lengih 2 m form the ceiling . A force of 50 N in the horizonlal direction is applied at the mid Point P of the rope as shown in figure. what is the angle the rope makes. with the vertical in equilibrium ?
Neglect mass of the rope:
![](data:image/png;base64,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)
Two bodies A and B cach of mass
are fixed together by a massless spring
force
acts on the mass B as shown in figure. At the instant shown, a body A has an accelcration a. what is the acceleration of B?
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)
Two bodies A and B cach of mass
are fixed together by a massless spring
force
acts on the mass B as shown in figure. At the instant shown, a body A has an accelcration a. what is the acceleration of B?
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)
A block of mass m=4 kg is placed over a rough inclined plane as shown in figure, The cocfficient of friction between the block and plane is s=0.6.A force F=10 N is applied on the block of an angle at 30° The contact force between the block and the plane is
![](data:image/png;base64,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)
A block of mass m=4 kg is placed over a rough inclined plane as shown in figure, The cocfficient of friction between the block and plane is s=0.6.A force F=10 N is applied on the block of an angle at 30° The contact force between the block and the plane is
![](data:image/png;base64,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)
If the unit vectors and
are inclined at an angle
such that
, then
lies in the interval
For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.
If the unit vectors and
are inclined at an angle
such that
, then
lies in the interval
For an interval, square bracket denotes close bracket and parantheses means open bracket. Close bracket means that point is included in the interval. Opem bracket means the point is not included in the interval.