MCQs of Vector Algebra

Vector Algebra MCQs

MCQs of Vector Algebra

Showing 181 to 190 out of 194 Questions

181.

\bar{a}

and

\bar{b}

are two unit vectors, then the vector

(\bar{a} + \bar{b}) \times (\bar{a} \times \bar{b})

is parallel to the vector _____ .

(a)	$\bar{a} + \bar{b}$
(b)	$\bar{a} - \bar{b}$
(c)	$2 \bar{a} + \bar{b}$
(d)	$2 \bar{a} - \bar{b}$

182.

For non-zero vectors

\bar{a}

\bar{b}

\bar{c}

|(\bar{a} \times \bar{b}) . \bar{c}| = |\bar{a}| |\bar{b}| |\bar{c}|

holds if and only if _____ .

(a)	$\bar{a} . \bar{b} = 0, \bar{b} . \bar{c} = 0$
(b)	$\bar{b} . \bar{c} = 0, \bar{c} . \bar{a} = 0$
(c)	$\bar{c} . \bar{a} = 0, \bar{a} . \bar{b} = 0$
(d)	$\bar{a} . \bar{b} = \bar{b} . \bar{c} = \bar{c} . \bar{a} = 0$

183.

If ABCDEF is a regular hexagon

\vec{A D} + \vec{E B} + \vec{F C}

= _____ .

(a)	2 $\vec{A B}$
(b)	$\bar{0}$
(c)	3 $\vec{A B}$
(d)	4 $\vec{A B}$

184.

\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

185.

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

186.

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°

187.

If the volume of the parallelopiped with co-terminus edges

4 \hat{i} + 5 \hat{j} + \hat{k}

- \hat{j} + \hat{k}

and

3 \hat{i} + 9 \hat{j} + p \hat{k}

is 34 cubic units, then p = _____ .

(a)	4
(b)	-13
(c)	13
(d)	6

188.

Let

\bar{a}

\bar{b}

and

\bar{c}

be non-zero vectors such that

(\bar{a} \times \bar{b}) \times \bar{c} = - \frac{1}{4} |\bar{b}| |\bar{c}| \bar{a}

. If θ is the acute angle between vectors

\bar{b}

and

\bar{c}

, then the measure of the angle between

\bar{a}

and

\bar{c}

is _____ .

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

189.

\bar{a} . \{(\bar{b} + \bar{c}) \times (\bar{a} + \bar{b} + \bar{c})\}

= _____ .

(a)	0
(b)	1
(c)	-1
(d)	None of the above

190.

Let

\bar{a}

\bar{b}

and

\bar{c}

be three vectors such that

\bar{c}

is perpendicular to both

\bar{a}

and

\bar{b}

|\bar{c}|

= 1 and the angle between

\bar{a}

and

\bar{b}

\frac{π}{4}

, then

{[\bar{a} \bar{b} \bar{c}]}^{2}

= _____ .

(a)	$\|\bar{a}\| \|\bar{b}\|$
(b)	${\|\bar{a}\|}^{2} {\|\bar{b}\|}^{2}$
(c)	$\bar{a} . \bar{b}$
(d)	$\frac{1}{2} {\|\bar{a}\|}^{2} {\|\bar{b}\|}^{2}$

Showing 181 to 190 out of 194 Questions