MCQs of સદિશનું બીજગણિત

સદિશનું બીજગણિત MCQs

MCQs of સદિશનું બીજગણિત

Showing 21 to 30 out of 187 Questions

21.

જો

|\bar{x} \cdot \bar{y}| = c o s α,

તો

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

_____.

(a)	$\pm s i n α$
(b)	$s i n α$
(c)	$- s i n α$
(d)	$\sin^{2} α$

22.

જો

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

તો

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

_____ જ્યાં

|\bar{x}| = 1 .

(a)	$\bar{x} \times \bar{y}$
(b)	$\bar{x}$
(c)	$- \bar{y}$
(d)	$\bar{y} \times \bar{x}$

23.

A(3, −1), B(2, 3) અને C(5, 1) હોય તો

m ∠ A =

______.

(a)	$c o s^{- 1} \frac{3}{\sqrt{34}}$
(b)	$π - c o s^{- 1} \frac{3}{\sqrt{34}}$
(c)	$s i n^{- 1} \frac{5}{\sqrt{34}}$
(d)	$\frac{π}{2}$

24.

જો

\bar{x} = \hat{i} - \hat{j} + \hat{k},

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

અને

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

સમતલીય હોય તથા

|\bar{z}| = \sqrt{3},

તો _____

(a)	$a = 1, b = - 1$
(b)	$a = 1, b = \pm 1$
(c)	$a = - 1, b = \pm 1$
(d)	$a = \pm 1, b = 1$

25.

\bar{a} \times \{\bar{b} \times (\bar{c} \times \bar{d})\}

= _____

(a)	$(\bar{b} \cdot \bar{a}) (\bar{c} \times \bar{d})$ - $(\bar{b} \cdot \bar{c}) (\bar{a} \times \bar{d})$
(b)	$(\bar{b} \cdot \bar{d}) (\bar{a} \times \bar{c})$ - $(\bar{b} \cdot \bar{c}) (\bar{a} \times \bar{d})$
(c)	$(\bar{b} \cdot \bar{c}) (\bar{a} \times \bar{d})$ - $(\bar{b} \cdot \bar{a}) (\bar{b} \times \bar{d})$
(d)	$(\bar{b} \cdot \bar{a}) (\bar{b} \times \bar{a})$ - $(\bar{c} \cdot \bar{d}) (\bar{c} \times \bar{d})$

26.

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

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

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

= _____

(a)	$2 [\bar{a} \bar{b} \bar{c}]$
(b)	$\bar{0}$
(c)	$\bar{a}$ + $\bar{b}$ + $\bar{c}$
(d)	0

27.

જો સદિશો

\bar{a} = 2 \overset{\land}{i} + \overset{\land}{j} - \overset{\land}{k}

અને

\bar{b}

સમરેખ હોય અને

\bar{a} \cdot \bar{b}

= 3 તો

\bar{b}

= _____

(a)	$(1, \frac{1}{2}, - \frac{1}{2})$
(b)	$(\frac{2}{3}, \frac{1}{3}, - \frac{1}{3})$
(c)	$(\frac{1}{2}, \frac{1}{4}, \frac{- 1}{4})$
(d)	(0, 0, 0)

28.

શૂન્યેતર એકમ સદિશો

\bar{x}

\bar{y}

માટે જો

2 (\bar{x} \cdot \bar{y})

|x| |y|

તો

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

= ?

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

29.

જો

|x|

|y|

= 1 અને

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

\frac{π}{6}

હોય તો

|x - y|

= _____

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

30.

3 (a \times b)

અને

\frac{1}{2} (b - (a \cdot b) a)

વચ્ચેનો ખૂણો છે.

(a)	30°
(b)	60°
(c)	90°
(d)	$\cos^{- 1} (\frac{3}{4})$

Showing 21 to 30 out of 187 Questions