MCQs of Vector Algebra

Showing 141 to 150 out of 194 Questions

141.

Measure of angle between \bar{a} and \bar{b} is 120^{˚} . If |\bar{a}| = 1, |\bar{b}| = 2 then value of {\{(\bar{a} + 3 \bar{b}) \times (3 \bar{a} - \bar{b})\}}^{2} is_____

142.

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}] =_____

143.

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

144.

\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 =_____

145.

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} =_____

146.

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}) =_____

147.

\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}_____

148.

(\bar{a} . (\bar{b} \times \bar{i})) \hat{i} + (\bar{a} . (\bar{b} \times \hat{j})) \hat{j} + (\bar{a} . (\bar{b} \times \hat{k})) \hat{k} =_____

149.

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 =_____

150.

\bar{a}, \bar{b}, \bar{c} are non - zero vectors . \bar{b} is not perpendicular to both \bar{a} and \bar{c}, (\bar{a} \times \bar{b}) \times \bar{c} = \bar{a} \times (\bar{b} \times \bar{c}) then

(a)	$\bar{a} and \bar{c} are non - collinear$
(b)	$\bar{a} and \bar{c} are always collinear$
(c)	$\bar{a} and \bar{c} are always orthogonal$
(d)	$\bar{a}, \bar{b}, \bar{c} are non - coplanar$

Showing 141 to 150 out of 194 Questions