MCQs of Vector Algebra

Showing 151 to 160 out of 194 Questions

151.

Vectors (x, x+1, x+2), (x+3, x+4, x+5) and (x+6, x+7, x+8) are coplanar, then

152.

In a parallelogram \bar{a} = 3 \bar{α} - \bar{β}, \bar{b} = \bar{α} + 3 \bar{β} . If |\bar{α}| = |\bar{β}| = 2 and \bar{α}^\bar{β} = \frac{π}{3}, then the length of its diagonal is_____

153.

A vector \bar{a} + \bar{b} divides the angle between the vectors \hat{a} and \hat{b}, then_____

154.

I f \bar{A}, \bar{B}, \bar{C} a r e n o n - c o p l a n a r v e c t o r s, t h e n \frac{\bar{A} . \bar{B} \times \bar{C}}{\bar{C} \times \bar{A} . \bar{B}} + \frac{\bar{B} . \bar{A} \times \bar{C}}{\bar{C} . \bar{A} \times \bar{B}} =_____

155.

\bar{p} = \bar{a} + \bar{b} and \bar{q} = \bar{a} - \bar{b} . If |\bar{a}| = |\bar{b}| = k and the angle between \bar{a} and \bar{b} is 60^{˚}, then |\bar{p} \times \bar{q}| =_____

156.

\bar{a} = 2 \hat{i} + 2 \hat{j} + \hat{k} and \bar{b} is such that \bar{a} . \bar{b} = 14 and \bar{a} \times \bar{b} = 3 \hat{i} + \hat{j} - 8 \hat{k}, then \bar{b} =_____

157.

Which of the following options is a unit vector in the direction of

(3 \hat{i} + 4 \hat{j} - 5 \hat{k}) + 2 (2 \hat{i} + \hat{j})

(a)	$\frac{7}{\sqrt{110}} \hat{i} - \frac{6}{\sqrt{110}} \hat{j} - \frac{5}{\sqrt{110}} \hat{k}$
(b)	$- \frac{7}{\sqrt{110}} \hat{i} - \frac{6}{\sqrt{110}} \hat{j} - \frac{5}{\sqrt{110}} \hat{k}$
(c)	$\frac{7}{\sqrt{110}} \hat{i} + \frac{6}{\sqrt{110}} \hat{j} - \frac{5}{\sqrt{110}} \hat{k}$
(d)	$\frac{5}{\sqrt{110}} \hat{i} + \frac{6}{\sqrt{110}} \hat{j} - \frac{5}{\sqrt{110}} \hat{k}$

158.

The position vector of P is (4, 5, -3) and the distance of P from XY, YZ and ZX planes are P₁, P₂ and P₃ respectively, then

\underset{i = 1}{\sum^{3}} P_{i}

= _____ .

159.

|\bar{x}|

|\bar{y}|

= 2 and

(\bar{x},^{\land} \bar{y})

= θ, then

|\bar{x} - \bar{y} cosθ|

= _____ .

160.

The projection of vector (-4, -2, 4) on (2, 1, 1) is _____ .

Showing 151 to 160 out of 194 Questions