Match List - I with List - II.

	List - I (Two given vector)		List - II (Projection of $\vec{a}$ on $\vec{b}$)
(A)	$\vec{a} = \hat{i} - \hat{j}$, $\vec{b} = \hat{i} + \hat{j}$	(I)	$\frac{2}{\sqrt{5}}$
(B)	$\vec{a} = \hat{i} + \hat{j}$, $\vec{b} = 2\hat{i} - \hat{k}$	(II)	0
(C)	$\vec{a} = \hat{j} + \hat{k}$, $\vec{b} = \hat{i} + \hat{k}$	(III)	$\sqrt{2}$
(D)	$\vec{a} = 2\hat{i} + 3\hat{j}$, $\vec{b} = \hat{i} - \hat{k}$	(IV)	$\frac{1}{\sqrt{2}}$

Choose the correct answer from the options given below :

The set of value of $x$ for which the angle between the $\vec{a} = 2x^2\hat{i} + 4x\hat{j} + \hat{k}$ and $\vec{b} = 7\hat{i} - 2\hat{j} + x\hat{k}$ is obtuse is :

Let $\vec{a} = \hat{i} + 4\hat{j} + 2\hat{k}$, $\vec{b} = 3\hat{i} - 2\hat{j} + 7\hat{k}$ and $\vec{c} = 2\hat{i} + \hat{j} + 4\hat{k}$. A vector $\vec{d}$ which is perpendicular to both $\vec{a}$ and $\vec{b}$, and $\vec{c} \cdot \vec{d} = 14$, is:

Area (in sq. units) of the triangle with vertices A (1,1,1) B (1,2,3) and C (2,3,1) is:

If $|\vec{a}| = 3$ and $|\vec{b}| = 4$, then a value of $\lambda$ for which $\vec{a} + \lambda\vec{b}$ and $\vec{a} - \lambda\vec{b}$ are perpendiculars is.

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:

Let $|\vec{a}| = 5, |\vec{b}| = 2$ and $\vec{a}\cdot\vec{b} = 6$, then the value of $|\vec{a} \times \vec{b}|$ is equal to