MCQs of Vector Algebra

Vector Algebra MCQs

MCQs of Vector Algebra

Showing 171 to 180 out of 194 Questions

171.

{|\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)	$\frac{13}{9}$

172.

|\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)	$\frac{\sqrt{6} + \sqrt{2}}{2}$

173.

|\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)	$3 \hat{i} - 4 \hat{j} - 12 \hat{k}$

174.

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)

175.

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 $\sqrt{3}$

176.

|\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)	$\sqrt{3}$

177.

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

and

(\bar{a}, \bar{b}) = \frac{π}{6}

, then are of parallelogram whose diagonals are

\bar{a} + 2 \bar{b}

and

2 \bar{a} + \bar{b}

is _____ .

(a)	$\frac{1}{2}$
(b)	$\frac{4}{3}$
(c)	$\frac{3}{4}$
(d)	$\frac{1}{4}$

178.

\bar{a}

\bar{b}

and

\bar{c}

are non-coplanar vectors. If vectors

\bar{p}

\bar{q}

and

\bar{r}

are such that

\bar{p} = \frac{\bar{b} \times \bar{c}}{[\bar{a} \bar{b} \bar{c}]}

\bar{q} = \frac{\bar{c} \times \bar{a}}{[\bar{a} \bar{b} \bar{c}]}

and

\bar{r} = \frac{\bar{a} \times \bar{b}}{[\bar{a} \bar{b} \bar{c}]}

, then

(\bar{a} + \bar{b}) . \bar{p} + (\bar{b} + \bar{c}) . \bar{q} + (\bar{c} + \bar{a}) . \bar{r}

= _____ .

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

179.

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

180.

\bar{a}

\bar{b}

and

\bar{c}

are a right handed triad of mutually perpendicular vectors of magnitude a, b, c then the value of

\bar{a}

\bar{b}

and

\bar{c}

[\bar{a} \bar{b} \bar{c}]

= _____ .

(a)	a²b²c²
(b)	0
(c)	$\frac{1}{2}$ abc
(d)	abc

Showing 171 to 180 out of 194 Questions