MCQs of Vector Algebra

Showing 61 to 70 out of 194 Questions

61.

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

62.

F o r w h i c h v a l u e o f m t h e a n g l e b e t w e e n 2 \overset{\land}{i} - m \overset{\land}{j} + 3 m \overset{\land}{k} a n d (1 + m) \overset{\land}{i} - 2 m \overset{\land}{j} + \overset{\land}{k} i s a c u t e

63.

A n g l e b e t w e e n \bar{a} = x \overset{\land}{i} - 3 \overset{\land}{j} - \overset{\land}{k} a n d \bar{b} = 2 x \overset{\land}{i} + x \overset{\land}{j} - \overset{\land}{k} i s a c u t e a n d a n g l e b e t w e e n \bar{b} a n d γ i s o b t u s e t h e n x =_____.

64.

I f s i d e s o f r e g u l a r h e x a g o n A B C D E F a r e \vec{A B} = \bar{a} a n d \vec{B C} = \bar{b} t h e n \vec{F A} =_____

65.

If ABCDF is regular hexagon

66.

I f f o r u n i t v e c t o r s \bar{a}, \bar{b}, \bar{c}, \bar{a} \times (\bar{b} \times \bar{c}) = \frac{\bar{b}}{2} a n d \bar{b} a n d \bar{c} a r e n o n - c o l l i n e a r v e c t o r s t h e n a m a k e s a n g l e_____a n d_____w i t h b a n d c r e s p e c t i v e l y .

67.

I f |\begin{matrix} a & a^{2} & 1 + a^{3} \\ b & b^{2} & 1 + b^{3} \\ c & c^{2} & 1 + c^{3} \end{matrix}| = 0 a n d v e c t o r s (1, a, a^{2}), (1, b, b^{2}) (1, c, c^{2}) a r e n o n - c o p l a n n a r, t h e n t h e p r o d u c t a b c e q u a l s .

68.

F o r a n y v e c t o r \bar{a} t h e v a l u e o f

{|\bar{a} \times \overset{\land}{i}|}^{2} + {|\bar{a} \times \overset{\land}{j}|}^{2} + {|\bar{a} \times \overset{\land}{k}|}^{2} =____

69.

I f (\bar{a} \times \bar{b}) \times \bar{c} = \bar{a} \times (\bar{b} \times \bar{c}) w h e r e \bar{a}, \bar{b} a n d \bar{c} a r e a n y t h r e e v e c t o r s s u c h t h a t \bar{a} \cdot \bar{b} \neq 0, \bar{b} \cdot \bar{c} \neq 0, t h e n \bar{a} a n d \bar{c} a r e

(a)	$i n c l i n e d a t a n a n g l e o f \frac{π}{3} b e t w e e n t h e m$
(b)	$i n c l i n e d a t a n a n g l e o f \frac{π}{6} b e t w e e n t h e m$
(c)	$P e r p e n d i c u l a r$
(d)	$p a r a l l e l$

70.

I f \bar{u}, \bar{v} a n d \bar{w} a r e n o n c o p l a n a r v e c t o r s a n d p, q a r e r e a l n u m b e r s, t h e n t h e e q u a l i t y [3 \bar{u} p \bar{v} p \bar{w}] - [p \bar{v} \bar{w} q \bar{u}] - [2 \bar{w} q \bar{v} q \bar{u}] = 0 h o l d s f o r :

(a)	exactlytwo value of (p,q)
(b)	more than two values but not all values of (p,q)
(c)	all value of (p,q)
(d)	exactly one value of (p,q)

Showing 61 to 70 out of 194 Questions