MCQs of Vector Algebra

Vector Algebra MCQs

MCQs of Vector Algebra

Showing 71 to 80 out of 194 Questions

71.

A line AB in three dimenstional space makes angle 45^ο and 120^ο with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis then θ equals

(a)	30^ο
(b)	45^ο
(c)	60^ο
(d)	75^ο

72.

I f \bar{a} = \frac{1}{\sqrt{10}} (3 \overset{\land}{i} + \overset{\land}{k}) a n d \bar{b} = \frac{1}{7} (2 \overset{\land}{i} + 3 \overset{\land}{j} - 6 \overset{\land}{k}) t h e n t h e v a l u e o f (2 \bar{a} - \bar{b}) \cdot [(\bar{a} \times \bar{b}) \times (\bar{a} + 2 \bar{b})] i s

(a)	-3
(b)	5
(c)	3
(d)	-5

73.

I f t h e v e c t o r s \vec{A B} = 3 \overset{\land}{i} + 4 \overset{\land}{k} a n d \vec{A C} = 5 \overset{\land}{i} - 2 \overset{\land}{j} + 4 \overset{\land}{k} a r e t h e s i d e s o f a △ A B C t h e n t h e l e n g t h e o f t h e m e d i a n t h r o u g h A i s

(a)	$\sqrt{18}$
(b)	$\sqrt{72}$
(c)	$\sqrt{33}$
(d)	$\sqrt{45}$

74.

I f \bar{a} a n d \bar{b} a r e n o i n c o l l i n e a r v e c t o r s, t h e n t h e v a l u e o f α f o r w h i c h t h e v e c t o r s \bar{u} = (α - 2) \bar{a} + \bar{b} a n d \bar{v} = (2 + 3 α) \bar{a} - 3 \bar{b} a r e c o l l i n e a r i s :

(a)	$\frac{3}{2}$
(b)	$\frac{2}{3}$
(c)	$- \frac{3}{2}$
(d)	$- \frac{2}{3}$

75.

Let ΔABC be a triangle with vertices at points A(2,3,5),B(-1,3,2) and C(λ,5,μ) in three dimensional space. If the median through A is equally inclined with the axes,then (λ,μ) is equal to

(a)	(10,7)
(b)	(7,5)
(c)	(7,10)
(d)	(5,7)

76.

L e t \bar{a} = 2 \overset{\land}{i} + \overset{\land}{j} - 2 \overset{\land}{k}, \bar{b} = \overset{\land}{i} + \overset{\land}{j} . I f \bar{c} i s a v e c t o r s u c h t h a t \bar{a} \cdot \bar{c} = |\bar{c}|, |\bar{c} - \bar{a}| = 2 \sqrt{2} a n d t h e a n g l e b e t w e e n \bar{a} \times \bar{b} a n d \bar{c} i s 30^{\circ} t h e n |(a \times b) \times c| e q u a l s

(a)	$\frac{1}{2}$
(b)	$\frac{3 \sqrt{3}}{2}$
(c)	3
(d)	$\frac{3}{2}$

77.

I f [\bar{a} \times \bar{b} \bar{b} \times \bar{c} \bar{c} \times \bar{a}] = λ {[\bar{a} \bar{b} \bar{c}]}^{2} t h e n λ i s e q u a l t o

(a)	0
(b)	1
(c)	2
(d)	3

78.

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 :

(a)	$4 \sqrt{2}$
(b)	12
(c)	24
(d)	$12 \sqrt{2}$

79.

I f \overset{\land}{x}, \overset{\land}{y} a n d \overset{\land}{z} a r e t h r e e u n i t v e c t o r s i n t h r e e - d i m e n s i o n a l s p a c e, t h e n t h e m i n i m u m v l a u e o f {|\overset{\land}{x} + \overset{\land}{y}|}^{2} + {|\overset{\land}{y} + \overset{\land}{z}|}^{2} + {|\overset{\land}{z} + \overset{\land}{x}|}^{2} i s :

(a)	$\frac{3}{2}$
(b)	3
(c)	$3 \sqrt{3}$
(d)	6

80.

L e t \bar{a}, \bar{b} a n d \bar{c} b e t h r e e n o n z e r o v e c t o r s s u c h t h a t n o t w o o f t h e m a r e c o l l i n e a r a n d (\bar{a} \times \bar{b}) \times \bar{c} = \frac{1}{3} |\bar{b}| |\bar{c}| \bar{a} . I f θ i s t h e a n g l e b e t w e e n v e c t o r s \bar{b} a n d \bar{c}, t h e n a v a l u e o f \sin θ i s :

(a)	$\frac{2 \sqrt{2}}{3}$
(b)	$\frac{- \sqrt{2}}{3}$
(c)	$\frac{2}{3}$
(d)	$\frac{2 \sqrt{3}}{3}$

Showing 71 to 80 out of 194 Questions