If $|\vec{a}| = 3|\vec{b}|$, $|\vec{b}| = 2$ and angle between $\vec{a}$ and $\vec{b}$ is $60^\circ$, then $|\vec{a} - \vec{b}|$ is equal to:

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors such that $\vec{a} + \vec{b} + \vec{c} = 0$. The value of $\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}$ is

If $\theta$ is an acute angle and the vector $\vec{a} = (\sin \theta)\vec{i} + (\cos\theta)\vec{j}$ is perpendicular to the vector $\vec{b} = i - \sqrt{3}j$ then $\theta$ is equal to

If $\lvert\vec{a}\rvert = \lvert\vec{b}\rvert = \lvert\vec{a}+\vec{b}\rvert = 1$, then

Match List-I with List-II

Choose the correct answer from the options given below:

The area of the parallelogram whose adjacent sides are determined by the vectors $\vec{a} = \hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = 2\hat{i} - 7\hat{j} + \hat{k}$ is :

If $-3 \leq k \leq 1$ and $|\vec{a}| = 2$ then $|k\vec{a}|$ is

The position vector of the point which divides the join of the points $2\vec{a}-3\vec{b}$ and $3\vec{a}-2\vec{b}$ externally in the ratio 2:3, is: