If $\theta$ is angle between $\vec{a}$ & $\vec{b}$, then for vectors $\vec{a}, \vec{b}$ and $\vec{c}$,

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\vec{a} \times \vec{b} = \vec{a} \times \vec{c}, \vec{a} \neq 0, \vec{b} \neq \vec{c}$	I.	$\theta = \dfrac{\pi}{4}$
B.	$\vec{a} \times \vec{b} = 0$	II.	$\vec{a} \parallel (\vec{b} - \vec{c})$
C.	$\vert \vec{a}.\vec{b} \vert = \vert \vec{a} \times \vec{b} \vert$	III.	$\vec{b} = \vec{c}$
D.	$\vec{a}.\vec{b} = \vec{a}.\vec{c}$ and $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$, $\vec{a} \neq 0$	IV.	$\vec{a} = 0, \vec{b} = 0$ or $\vec{a} \parallel \vec{b}$

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A vector $\vec{a}$ of magnitude $3\sqrt{2}$ making an angle of $\frac{\pi}{3}$ with $\hat{i}$, $\frac{\pi}{4}$ with $\hat{j}$ and an actue angle $\theta$ with $\hat{k}$, is

If $\vec{a} = 2\hat{i} - 2\hat{j} + \hat{k}$, then which of the following statements are TRUE?

(A) unit vector along $\vec{a}$ is $\frac{1}{3}(2\hat{i}+2\hat{j}-\hat{k})$

(B) $|3\vec{a}| = 9$

(C) $\vec{a}$ is perpendicular to $2\hat{i}+3\hat{j}+2\hat{k}$

(D) Direction Ratios of $\vec{a}$ are 2,-2,1

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The position vector of a point R which divides the line joining two points P and Q whose position vectors are $\hat{i} + 2\hat{j} - \hat{k}$ and $-\hat{i} + \hat{j} + \hat{k}$ respectively in the ratio 2 : 1 externally is :

If $|\vec a|=2, |\vec b|=7$ and $\vec a\times\vec b=3\hat i+2\hat j+6\hat k$, then angle between $\vec a$ and $\vec b$ is:

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

If $\hat{i}$, $\hat{j}$ and $\hat{k}$ are unit vectors along the co-ordinate axes OX, OY and OZ respectively, then

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

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

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

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

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