MCQs of Vector Algebra

Vector Algebra MCQs

MCQs of Vector Algebra

Showing 91 to 100 out of 111 Questions

91.

The projection of vector (-4, -2, 4) on (2, 1, 1) is _____ .

(a)	(1, -1, -2)
(b)	(-2, -1, -1)
(c)	(-2, 1, 1)
(d)	(-1, 1, 2)

92.

Magnitude of the projection vector of (4, 1, 3) on (1, -2, 3) is _____ .

(a)	$\frac{15}{14}$
(b)	$\frac{11}{14}$
(c)	$\frac{11}{\sqrt{14}}$
(d)	$\frac{15}{\sqrt{14}}$

93.

|\bar{x}|

= 3,

|\bar{y}|

= 4 and

\bar{x} ⊥ \bar{y}

, then

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

= _____ .

(a)	0
(b)	12
(c)	3
(d)	1

94.

\bar{x}

= (1, -1, 0),

\bar{y}

= (0, 1, 3) and

\bar{z}

= (2, 1, 1) then

\bar{x} \times (\bar{y} \times \bar{z})

= _____ .

(a)	(2, 2, 4)
(b)	(4, 4, 2)
(c)	(-2, 2, 4)
(d)	(2, 4, 2)

95.

For unit vectors

\bar{a}

and

\bar{b}

\bar{a} + \bar{b} = \bar{0}

, then

\bar{a} . \bar{b}

= _____ .

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

96.

\vec{A B} = \hat{i} + 2 \hat{j} + 3 \hat{k}

and

\vec{A C} = - 3 \hat{i} + 2 \hat{j} + \hat{k}

then area of ΔABC = _____ .

(a)	45
(b)	3 $\sqrt{5}$
(c)	$\frac{3}{2} \sqrt{5}$
(d)	5 $\sqrt{3}$

97.

If for non-zero unit vectors

\bar{x}

and

\bar{y}

2 (\bar{x} . \bar{y}) = |\bar{x}| . |\bar{y}|

, then

(\bar{x},^{\land} \bar{y})

= _____ .

(a)	$\frac{π}{2}$
(b)	$\frac{π}{6}$
(c)	$\frac{π}{3}$
(d)	0

98.

\bar{x}

= (1, 1, 2),

\bar{y}

= (1, 2, 1) and

\bar{z}

= (2, 1, 1), then

\bar{x} \times (\bar{y} \times \bar{z})

= _____ .

(a)	(-5, 5, 0)
(b)	(5, 5, 5)
(c)	(5, 0, -5)
(d)	(-5, -5, -5)

99.

For unit vectors

\bar{x}

and

\bar{y}

, if

\bar{x} . \bar{y} = 0

then _____ .

(a)	$\|\bar{x} + \bar{y}\| = \sqrt{2}$
(b)	$\|\bar{x} + \bar{y}\| = 2$
(c)	$\|\bar{x} + \bar{y}\| = \sqrt{3}$
(d)	$\|\bar{x} + \bar{y}\| = 1$

100.

{|\bar{x} \times \bar{y}|}^{2} = 169 - {(\bar{x} . \bar{y})}^{2}

and

|\bar{x}|

= 9, then

|\bar{y}|

= _____ .

(a)	$\frac{169}{9}$
(b)	$\frac{9}{13}$
(c)	$\frac{169}{81}$
(d)	$\frac{13}{9}$

Showing 91 to 100 out of 111 Questions