MCQs of Vector Algebra

Vector Algebra MCQs

MCQs of Vector Algebra

Showing 101 to 110 out of 111 Questions

101.

|\bar{x}| = |\bar{y}| = 1

and

(\bar{x},^{\land} \bar{y}) = \frac{π}{6}

, then

|\bar{x} - \bar{y}|

= _____ .

(a)	$\frac{\sqrt{6} - \sqrt{2}}{4}$
(b)	1
(c)	$\frac{\sqrt{6} - \sqrt{2}}{2}$
(d)	$\frac{\sqrt{6} + \sqrt{2}}{2}$

102.

|\bar{x}|

= 13 and whose direction angles are

\cos^{- 1} \frac{3}{13}

\cos^{- 1} \frac{4}{13}

and

\cos^{- 1} \frac{12}{13}

, then

\bar{x}

= _____ .

(a)	$3 \hat{i} + 4 \hat{j} - 12 \hat{k}$
(b)	$3 \hat{i} + 4 \hat{j} + 12 \hat{k}$
(c)	$3 \hat{i} - 4 \hat{j} + 12 \hat{k}$
(d)	$3 \hat{i} - 4 \hat{j} - 12 \hat{k}$

103.

The unit vector perpendicular to (cosα, sinα) in R² is

\bar{y}

= _____ .

(a)	$(\cos \frac{α}{2}, \sin \frac{α}{2})$
(b)	(-cosα, -sinα)
(c)	(-sinα, cosα)
(d)	(cosα, sinα)

104.

For

\bar{a} = 3 \hat{i} + 4 \hat{j} + \hat{k}

and

\bar{b} = \hat{i} + \hat{j} + \hat{k}

{comp}_{\bar{b}} \bar{a}

= _____ .

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

105.

|\bar{a}|

= 5,

|\bar{b}|

= 9 and

|\bar{a} + \bar{b}|

= 10

\sqrt{2}

then

|\bar{a} - \bar{b}|

= _____ .

(a)	2 $\sqrt{3}$
(b)	12
(c)	3 $\sqrt{2}$
(d)	$\sqrt{3}$

106.

If the measure of the angle between vectors

\bar{a}

and

\bar{b}

is θ and

|\bar{a} \times \bar{b}| = |\bar{a} . \bar{b}|

then θ = _____ .

(a)	0
(b)	$\frac{π}{4}$
(c)	$\frac{π}{2}$
(d)	π

107.

\bar{a}

and

\bar{b}

are unit vector such that

\bar{a} . \bar{b}

= cos θ, then

|\bar{a} + \bar{b}|

= _____ .

(a)	2 sin $\frac{θ}{2}$
(b)	2 sinθ
(c)	2 cos $\frac{θ}{2}$
(d)	2 cosθ

108.

Three vectors

\bar{a}

\bar{b}

and

\bar{c}

are such that

\bar{a}

≠

\bar{0}

and

\bar{a} \times \bar{b} = 2 \bar{a} \times \bar{c}

|\bar{a}| = |\bar{c}| = 1

|\bar{b}| = 4

and

|\bar{b} \times \bar{c}| = \sqrt{15}

. If

\bar{b} - 2 \bar{c} = λ \bar{a}

, then λ = _____ .

(a)	1
(b)	-4
(c)	2
(d)	-2

109.

Vectors

\bar{a}

and

\bar{b}

are such that

|\bar{a}| = 3 \sqrt{3}

|\bar{b}| = 4

and

|\bar{a} + \bar{b}| = \sqrt{7}

, then the measure of the angle between

\bar{a}

and

\bar{b}

is _____ .

(a)	120°
(b)	60°
(c)	30°
(d)	150°

110.

\bar{a} = p \hat{i} - \hat{j} + 8 \hat{k}

and

\bar{b} = 2 \hat{i} + 4 \hat{j} + q \hat{k}

and

(\bar{a} + 3 \bar{b}) \times (3 \bar{a} - \bar{b}) = \bar{0}

, then p - q = _____ .

(a)	$\frac{63}{2}$
(b)	$\frac{63}{4}$
(c)	$- \frac{63}{2}$
(d)	$- \frac{17}{32}$

Showing 101 to 110 out of 111 Questions