MCQs of Vector Algebra

Showing 51 to 60 out of 194 Questions

51.

\bar{c} i s t h e v e c t o r i n t h e d i r e c t i o n o f i n t e r n a l b i s e c t o r o f a n g l e b e t w e e n \bar{a} = 7 \overset{Λ}{i} - 4 \overset{Λ}{j} - 4 \overset{Λ}{k} a n d \bar{b} = 2 \overset{Λ}{i} - \overset{Λ}{j} + 2 \overset{Λ}{k} w h e r e |\bar{c}| = 5 \sqrt{6} t h e n c =_____

(a)	$\frac{5}{3} (\overset{Λ}{i} + 7 \overset{Λ}{j} + 2 \overset{Λ}{k})$
(b)	$\frac{5}{3} (- 5 \overset{Λ}{i} + 5 \overset{Λ}{j} + 2 \overset{Λ}{k})$
(c)	$\frac{5}{3} (\overset{Λ}{i} - 7 \overset{Λ}{j} + 2 \overset{Λ}{k})$
(d)	$\frac{5}{3} (5 \overset{Λ}{i} + 5 \overset{Λ}{j} + 2 \overset{Λ}{k})$

52.

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

53.

3 \overset{\land}{i} + \overset{\land}{j} - 2 \overset{\land}{k} a n d \overset{\land}{i} + 3 \overset{\land}{j} + 4 \overset{\land}{k} a r e t h e c o r r e s p o n d i n g v e c t o r s o f t h e d i a g o n a l s o f p a r a l l e l o r a m, t h e n a r e a o f p a r a l l e \log r a m i s =_____

54.

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 ?

55.

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_____

56.

I f \bar{a} = \overset{\land}{i} + \overset{\land}{j} + \overset{\land}{k}, \overset{\land}{b} = 4 \overset{\land}{i} + 3 \overset{\land}{j} + 4 \overset{\land}{k} a n d \bar{c} = \overset{\land}{i} + α \overset{\land}{j} + β \overset{\land}{k} a r e l i n e a r l y d e p e n d e n t v e c t o r s a n d |\bar{c}| = \sqrt{3} t h e n,_____

57.

I f p o s i t i o n v e c t o r s o f v e r t i c e s o f ∆ A B C a r e \bar{a}, \bar{b} a n d \bar{c} t h e n u n i t v e c t o r p e r p e n d i c u l r t o i t s p l a n e i s

(a)	$\bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a}$
(b)	$\frac{\bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a}}{\|\bar{a} \times \bar{b} + \bar{b} \times \bar{c} + \bar{c} \times \bar{a}\|}$
(c)	$\frac{\bar{a} \times \bar{b}}{\|\bar{a} \times \bar{b}\|}$
(d)	none of these

58.

U n i t v e c t o r p e r p e n d i c u l a r t o 5 \overset{\land}{i} + 2 \overset{\land}{j} + 6 \overset{\land}{k} a n d v e c t o r o f p l a n e o f 2 \overset{\land}{i} + \overset{\land}{j} + \overset{\land}{k}, \overset{\land}{i} - \overset{\land}{j} + \overset{\land}{k} i s

(a)	$\frac{6 \overset{\land}{i} - 5 \overset{\land}{k}}{\sqrt{61}}$
(b)	$\frac{3 \overset{\land}{j} - \overset{\land}{k}}{\sqrt{10}}$
(c)	$\frac{2 \overset{\land}{i} + 5 \overset{\land}{k}}{\sqrt{29}}$
(d)	$\frac{2 \overset{\land}{i} - \overset{\land}{j} - 2 \overset{\land}{k}}{3}$

59.

U n i t v e c t o r c o p l a n a r w i t h v e c t o r \overset{\land}{i} + \overset{\land}{j} + 2 \overset{\land}{k} a n d \overset{\land}{i} + 2 \overset{\land}{j} + \overset{\land}{k} a n d p e r p e n d i c u l a r t o \overset{\land}{i} - \overset{\land}{j} + \overset{\land}{k} i s =_____.

(a)	$\frac{\overset{\land}{k} - \overset{\land}{j}}{\sqrt{2}}$
(b)	$\frac{\overset{\land}{i} + \overset{\land}{j} + \overset{\land}{k}}{\sqrt{3}}$
(c)	$\frac{\overset{\land}{i} + \overset{\land}{j} + 2 \overset{\land}{k}}{\sqrt{6}}$
(d)	$\frac{\overset{\land}{i} + 2 \overset{\land}{j} + \overset{\land}{k}}{\sqrt{6}}$

60.

Measure of projection of a line segment on axis are respectively 12,4 and 3 then lenth of line segment is _____

Showing 51 to 60 out of 194 Questions