MCA Entrance Previous Year Question Bank

If $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{a}\cdot \vec{b}=1$ and $\vec{a}\times \vec{b}=\hat{j}\hat{k}$, then $\vec{b}$ is equal to:

If $\vec{a},\vec{b}$ and $\vec{c}$ are unit vectors, then $|\vec{a}-\vec{b}{|}^2+|\vec{b}-\vec{c}{|}^2+|\vec{c}-\vec{a}{|}^2$ does not exceed:

If $\vec{a}$ and $\vec{b}$ are two unit vectors such that $\vec{a}+2\vec{b}$ and $5\vec{a}-4\vec{b}$ are perpendicular to each other, then the angle between $\vec{a}$ and $\vec{b}$ is:

The unit vectors orthogonal to the vector $-\hat{i}+2\hat{j}+2\hat{k}$ and making equal angles with x and y axis are

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R

$\text{Assertion A: If dot product and cross product of }\vec{A}\text{ and }\vec{B}\text{ are zero, it implies that one of the vectors }\vec{A}\text{ and }\vec{B}\text{ must be null vector}$

Reason R: Null vector is a vector with a zero magnitude

In the light of the above statements, choose the correct answer from the options given below:

Each of the angle between vectors $\vec{a}$,$\vec{b}$ and $\vec{c}$ is equal to $60^{\circ }$ if $|\vec{a}|=4$,$|\vec{b}|=2$ and $|\vec{c}|=6$ then the modulus of $\vec{a}+\vec{b}+\vec{c}$ is

If ${\hat{n}}_1,{\hat{n}}_2$ are two unit vectors and $\theta$ is the angle between them, then $\cos \frac{\theta }{2}$ is equal to

Match List I with List II

Choose the correct answer from the options given below:

The moment of the couple formed by the forces $5\hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $-5\hat{\mathbf{i}}-\hat{\mathbf{k}}$ acting at the points (9,-1,2) and (3,-2,1) respectively, is

If the unit vectors $\vec{a}$ and $\vec{b}$ are inclined at an angle $2\theta$ such that |\vec{a}-\vec{b}|<1 and $0\le \theta \le \pi$, then $\theta$ lies in the interval