MCQs of Vector Algebra

Showing 31 to 40 out of 194 Questions

31.

Vector of XZ - plane perpendicular to (2, 4, -3) and is

32.

I f a n g l e b e t w e e n \bar{a} a n d \bar{b} i s θ t h e n |\bar{a} - \bar{b}| =_____

33.

I f |\bar{a} + \bar{b}| = |\bar{a} - \bar{b}| t h e n v e c t o r \bar{a} a n d \bar{b}

34.

I f {|\bar{a} + \bar{b}|}^{2} = {|\bar{a}|}^{2} + {|\bar{b}|}^{2} t h e n

35.

I f \bar{a} = \overset{\land}{i} + \overset{\land}{j} + \overset{\land}{k}, \bar{b} = \overset{\land}{i} - \overset{\land}{j} + \overset{\land}{k} a n d \bar{c} i s u n i t v e c t o r p e r p e n d i c u l a r t o \bar{a} a n d \bar{b}, t h e n u n i t v e c t o r t o b o t h \bar{a} a n d \bar{c} i s_____

(a)	$\frac{1}{\sqrt{6}} (2 \overset{\land}{i} - \overset{\land}{j} + \overset{\land}{k})$
(b)	$\frac{1}{\sqrt{2}} (\overset{\land}{i} + \overset{\land}{j})$
(c)	$\frac{1}{\sqrt{2}} (\overset{\land}{j} + \overset{\land}{k})$
(d)	$\frac{1}{\sqrt{2}} (\overset{\land}{i} + \overset{\land}{k})$

36.

I f \bar{a}, \bar{b} a n d \bar{c} a r e n o n - c o p l a n a r v e c t o r s a n d \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}]}, \bar{r} = \frac{\bar{a} \times \bar{b}}{[\bar{a} \bar{b} \bar{c}]} t h e n (\bar{a} + \bar{b} + \bar{c}) \cdot (\bar{p} + \bar{q} + \bar{r}) =______

37.

I f p o i n t s p (\bar{a} + \bar{b} - \bar{c}), Q (2 \bar{a} + \bar{b}) a n d R (\bar{b} + \bar{t c}) a r e c o l i n e a r t =______w h e r e \bar{a} \bar{, b}, \bar{c} a r e n o n - c o p l a n a r v e c t o r s .

38.

T h e p o i n t s w h o s e p o s i t i o n v e c t o r s a r e 20 \overset{\land}{i} + p \overset{\land}{j}, 5 \overset{\land}{i} - \overset{\land}{j} a n d 10 \overset{\land}{i} - 13 \overset{\land}{j} a r e c o l l i n e a r t h e p =_____

39.

I f \bar{a}, \bar{b}, \bar{c} a r e c o p l a n a r u n i t v e c t o r s t h e n [2 \bar{a} - \bar{b} 2 \bar{b} - \bar{c} 2 \bar{c} - \bar{a}] =_____

40.

I f \bar{A}, \bar{B} a n d \bar{C} a r e t h r e e n o n - c o p l a n a r v e c t o r s t h e n \frac{\bar{A} \cdot (\bar{B} \times \bar{C})}{(\bar{C} \times \bar{A}) \cdot \bar{B}} + \frac{\bar{B} \cdot (\bar{A} \times \bar{C})}{\bar{C} \cdot (\bar{A} \times \bar{B})} =______

Showing 31 to 40 out of 194 Questions