MCQs of Vector Algebra

Showing 81 to 90 out of 111 Questions

81.

If \bar{a}, \bar{b}, \bar{c} are non - coplanar v e c t o r s, t h e n [\bar{a} \times \bar{b}, \bar{b} \times \bar{c}, \bar{c} \times \bar{a}] =_____

82.

If {(\bar{a} \times \bar{b})}^{2} + {(\bar{a} . \bar{b})}^{2} = 144, |\bar{a}| = 4, then |\bar{b}| =_____

83.

\bar{a} + 2 \bar{b} + 3 \bar{c} = 0 and \bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a} = λ (\bar{b} \times \bar{c}) then λ =_____

84.

If \bar{a} is any unit vector, then {|\bar{a} \times \bar{i}|}^{2} + {|\bar{a} \times \bar{j}|}^{2} + {|\bar{a} \times \bar{k}|}^{2} =_____

85.

If \bar{a} is any unit vector, then \hat{i} \times (\bar{A} \times \hat{i}) + \hat{j} \times (\bar{A} \times \hat{j}) + \hat{k} \times (\bar{A} \times \hat{k}) =_____

86.

\bar{a}, \bar{b} and \bar{c} are unit vector and a \times (\bar{b} \times \bar{c}) = \frac{\bar{b} + \bar{c}}{\sqrt{2}} then measure between \bar{a} and \bar{b}_____

87.

3 \bar{a} - 5 \bar{b} and 2 \bar{a} + \bar{b} are orthogonal vectors . \bar{a} + 4 \bar{b} and - \bar{a} + \bar{b} are also perpendicular to each other . If θ is an angle between the vectors \bar{a} and \bar{b}, then cosθ =_____

88.

\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}| =_____

89.

\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} =_____

90.

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)	$\frac{5}{\sqrt{110}} \hat{i} + \frac{6}{\sqrt{110}} \hat{j} - \frac{5}{\sqrt{110}} \hat{k}$

Showing 81 to 90 out of 111 Questions