MCQs of Vector Algebra

Showing 31 to 40 out of 111 Questions

31.

W h a t w i l l b e t h e m a g n i t u d e o f t h e p r o j e c t i o n o f \overset{Λ}{i} + \overset{Λ}{j} + \overset{Λ}{k} o n v e c t o r \overset{Λ}{j} ?

32.

I f A (1, 0, 0), B (0, 1, 0), C (0, 0, 1) a r e v e r t i c e s o f t r i a n g l e A B C t h e n m ∠ A =_____

33.

I f f o r ∆ A B C, \vec{B C} = \bar{a} \vec{C A} = \bar{b} a n d \vec{A B} = \bar{c} t h e n

(a)	$\bar{a} \cdot \bar{b} + \bar{b} \cdot \bar{c} + \bar{c} \cdot \bar{a} = 0$
(b)	$\bar{a} \times \bar{b} = \bar{b} \times \bar{c} = \bar{c} \times \bar{a}$
(c)	$\bar{a} \cdot \bar{b} = \bar{b} \cdot \bar{c} = \bar{c} \cdot \bar{a}$
(d)	$(\bar{a} \times \bar{b}) + (\bar{b} \times \bar{c}) + (\bar{c} \times \bar{a}) = 0$

34.

F i n d t h e a r e a o f t h e p a r a l l e \log r a m w h o s e s i d e s h a v e \overset{Λ}{i} a n d \overset{Λ}{i} + \overset{Λ}{j} a s c o r r e s p o n d i n g v e c t o r s ?

35.

F o r p a r a l l e \log r a m A B C D, i f \vec{A B} = \bar{a} a n d \vec{B C} = \bar{b} t h e n i t s a r e a i s_____

36.

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 .

37.

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} =____

38.

I f {|\bar{c}|}^{2} = 60 a n d |\bar{c}| \times (\overset{\land}{i} + 2 \overset{\land}{j} + 5 \overset{\land}{k}) = \bar{0}, t h e n a v a l u e o f \bar{c} \cdot (- 7 \overset{\land}{i} + 2 \overset{\land}{j} + 3 \overset{\land}{k}) i s :

39.

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 :

40.

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 :

Showing 31 to 40 out of 111 Questions