If the points P, Q, R with position vectors $5\hat{i} + \lambda\hat{j}$, $20\hat{i} - \hat{j}$ and $15\hat{i} - 6\hat{j}$ respectively are collinear, then the value of $\lambda$ is

If $\hat{a}, \hat{b}$ and $\hat{c}$ are three unit vectors and $\hat{a} + \hat{b} + \hat{c} = \vec{0}$, then the angle between $\hat{a}$ and $(-\hat{b})$ is

If $\theta$ is the angle between two unit vectors $\hat{a}$ and $\hat{b}$ then $|\hat{a}-\hat{b}| =$

If $\theta$ is the acute angle between two unit vectors $\vec{a}$ and $\vec{b}$, then $\cos\frac{\theta}{2} =$

If $\vec a\times\vec b=\vec a\times\vec c$ and $\vec a\neq\vec 0$, then which of the following is/are TRUE?

A. $\vec b=\vec c$

B. $\vec b+\vec c=\vec 0$

C. $\vec b=\vec c+\lambda\vec a$ for some scalar λ

D. $\vec b+\vec c=\lambda\vec a$ for some scalar λ

Choose the correct answer from the options given below:

If the vectors $\vec{a} = 3\hat{i} - p\hat{j} + 5\hat{k}$ and $\vec{b} = -6\hat{i} + 14\hat{j} + q\hat{k}$ are collinear, then the value of p and q are:

If $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along co-ordinates axes OX, OY and OZ respectively, then which of the following is/are true?

(A) $\hat{i} \times \hat{i} = \vec{0}$

(B) $\hat{i} \times \hat{k} = \hat{j}$

(C) $\hat{i} \cdot \hat{i} = 1$

(D) $\hat{i} \cdot \hat{j} = 0$

Choose the correct answer from the options given below: