If for two vectors $\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$$\stackrel{\to }{\mathrm{A}}×\stackrel{\to }{\mathrm{B}}=0$, then the vectors:

1. are perpendicular to each other.

2. are parallel to each other.

3. act at an angle of $60°.$

4. act at an angle of $30°.$

Subtopic:  Vector Product |
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$\stackrel{\to }{\mathrm{A}}$ and $\stackrel{\to }{\mathrm{B}}$ are two vectors and θ is the angle between them. If $\left|\stackrel{\to }{\mathrm{A}}×\stackrel{\to }{\mathrm{B}}\right|=\sqrt{3}\left(\stackrel{\to }{A}.\stackrel{\to }{B}\right)$, then the value of θ will be:

1. 60o

2. 45o

3. 30o

4. 90o

Subtopic:  Scalar Product | Vector Product |
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The linear velocity of a rotating body is given by $\stackrel{\to }{\mathrm{v}}=\stackrel{\to }{\mathrm{\omega }}×\stackrel{\to }{\mathrm{r}}$, where $\mathrm{\omega }$ is the angular velocity and r is the radius vector. The angular velocity of a body, $\stackrel{\to }{\mathrm{\omega }}=\stackrel{^}{\mathrm{i}}-2\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$ and their radius vector is   will be:

1.

2.

3.

4.

Subtopic:  Vector Product |
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If and , then

1.  1

2.  $\sqrt{65}$

3.  8

4.  4

Subtopic:  Vector Product |
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If  and  = , then

1.

2.

3.  $\stackrel{\to }{\mathrm{A}}$ is antiparallel to $\stackrel{\to }{\mathrm{B}}$

4.  $\stackrel{\to }{\mathrm{A}}$ is inclined to $\stackrel{\to }{\mathrm{B}}$ at an angle of 45$°$

Subtopic:  Vector Product |
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The scalar and vector product of two vectors,  and  is equal to:

1.  -25 & $\left(7\stackrel{^}{\mathrm{i}}-\stackrel{^}{\mathrm{j}}-5\stackrel{^}{\mathrm{k}}\right)$

2.  25 & $\left(-7\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}-5\stackrel{^}{\mathrm{k}}\right)$

3.  0 & $\left(-7\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}+3\stackrel{^}{\mathrm{k}}\right)$

4.  -25 & $\left(-7\stackrel{^}{\mathrm{i}}+\stackrel{^}{\mathrm{j}}+5\stackrel{^}{\mathrm{k}}\right)$

Subtopic:  Vector Product |
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Which of the following option is not true, if  and , where A and B are the magnitudes of ?

1.

2.

3.

4. A = 5

Subtopic:  Vector Product |
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1. ${\left({\mathrm{A}}^{2}+{\mathrm{B}}^{2}+\frac{\mathrm{AB}}{\sqrt{3}}\right)}^{1/2}$

2. A+B

3. ${\left({\mathrm{A}}^{2}+{\mathrm{B}}^{2}+\sqrt{3}\mathrm{AB}\right)}^{1/2}$

4. ${\left({\mathrm{A}}^{2}+{\mathrm{B}}^{2}+\mathrm{AB}\right)}^{1/2}$

Subtopic:  Scalar Product | Vector Product |
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Given are two vectors,   and . What should be the value of c so that vector  would become parallel to each other?

1.  1

2.  2

3.  3

4.  4

Subtopic:  Vector Product |
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The angle between vectors $\left(\stackrel{\to }{\mathrm{A}}×\stackrel{\to }{\mathrm{B}}\right)$ and $\left(\stackrel{\to }{\mathrm{B}}×\stackrel{\to }{\mathrm{A}}\right)$ is

1. Zero

2. $\mathrm{\pi }$

3. $\mathrm{\pi }/4$

4. $\mathrm{\pi }/2$

Subtopic:  Vector Product |
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