MCQs of Vector Algebra

Showing 81 to 90 out of 194 Questions

81.

L e t \bar{a} a n d \bar{b} b e t w o u n i t v e c t o r s s u c h t h a t |\bar{a} + \bar{b}| = \sqrt{3 .} I f \bar{c} = \bar{a} + 2 \bar{b} + 3 (\bar{a} \times \bar{b}), t h e n 2 |\bar{c}| i s e q u a l t o :

82.

L e t \bar{a}, \bar{b} a n d \bar{c} b e t h r e e u n i t v e c t o r s s u c h t h a t \bar{a} \times (\bar{b} \times \bar{c}) = \frac{\sqrt{3}}{2} (\bar{b} + \bar{c}) I f \bar{b} i s n o t p a r a l l e l t o \bar{c}, t h e n t h e a n g l e b e t w e e n \bar{a} a n d \bar{b} i s :

83.

L e t A B C b e a t r i a n g l e w h o s e c i r c u m c e n t r e i s a t P . I f t h e p o s i t i o n v e c t o r s o f A, B, C a n d P a r e \bar{a}, \bar{b}, \bar{c} a n d \frac{\bar{a} + \bar{b} + \bar{c}}{4} r e s p e c t i v e l y, t h e n t h e p o s i t i o n v e c t o r o f t h e o r t h o c e n t r e o f t h i s t r i a n g l e, i s :

84.

_____ is not a unit vector

(α \neq \frac{n π}{2}, n \in Z)

85.

\bar{x} = (a, 8, 3 a) a n d \bar{y} = (3 a, - 3, a)

are perpendicular to each other, then a = _____.

86.

If \bar{x} = (2, 3, 3), \bar{y} = (- 2, - 3, k), k \neq - 3, then |\bar{x} \cdot \bar{y}|

_____

|\bar{x}| |\bar{y}|

87.

The area of the parallelogram whose diagonal are

\hat{i} + \hat{j} + \hat{k} a n d \hat{i} - \hat{j} + \hat{k}

is _____.

88.

The area of the parallelogram whose adjacent sides are

\hat{i} + \hat{j} + \hat{k} a n d \hat{i} - \hat{j} + \hat{k}

is _____.

89.

_____ is not unit vector

(α \neq \frac{n π}{2}, n \in Z)

90.

\bar{x}

= (a, 8, 3a) and

\bar{y}

= (3a, -3, a) are perpendicular to each other, then a = _____ .

Showing 81 to 90 out of 194 Questions