MCQs of Vector Algebra

Vector Algebra MCQs

MCQs of Vector Algebra

Showing 161 to 170 out of 194 Questions

161.

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)	$\frac{15}{\sqrt{14}}$

162.

|\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

163.

\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)

164.

For the vectors

\bar{x}

and

\bar{y}

[2 \bar{x} + 3 \bar{y} \bar{x} \bar{y}]

= _____ .

(a)	0
(b)	6 $(\bar{x} \times \bar{y})$
(c)	6 ${\|\bar{x}\|}^{2}$
(d)	1

165.

If α, β, γ are the direction angles of

\bar{x}

, then cos 2α + cos 2β + cos 2γ = _____ .

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

166.

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

167.

\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 $\sqrt{3}$

168.

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

169.

\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)

170.

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)	$\|\bar{x} + \bar{y}\| = 1$

Showing 161 to 170 out of 194 Questions