Test Details

Vector Algebra

Feb 03, 12:40 PM

40 minutes

Feb 03, 1:20 PM

40.0 marks

MCQ

20 questions

vikas

Class Details

maths

Maths

class 12A

maths

Maths

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Question Text

Question 2 :
If $\bar{a}$ is unit vector, then $|\bar{a}\times \hat{i}|^2+|\bar{a}\times \hat{j}|^2+|\bar{a}\times \hat{k}|^2=$ _____________.

Question 3 :
A straight line is inclined to the axes of $Y$ and $Z$ at angles $45^{\circ}$ and $60^{\circ}$ respectively. The inclination of the line with the $X$-axis is

Question 4 :
When a body is thrown up, the sign of $g$ is positive when it goes up.

Question 5 :
If $|\overrightarrow{a}| = 5, |\overrightarrow{a} - \overrightarrow{b}|=8$ and $|\overrightarrow{a} + \overrightarrow{b}| = 10$, then $|\overrightarrow{b}|$ is equal to:

Question 6 :
If the position vectors of the points $A, B, C, D$ are$(0,2, 1)$, $(3,1,1),$ $(-5,3,2)$,$(2,4,1)$ respectively and if $PA+PB+PC+PD=0$ then the position vector of P is

Question 7 :
If the points $A$ and $B$ are $\left( 1,2,-1 \right)$ and $\left( 2,1,-1 \right)$ respectively, then $\vec { AB } $ is

Question 8 :
If $\vec{a} = (2, 1, -1),\vec{b} = (1,-1,0),\vec{c} = (5, -1, 1) $ ,then what is the unit vector parallel to $ \vec{a} + \vec{b} - \vec{c} $in the opposite direction ?

Question 9 :
Let a,b be two noncoffinear vectors. If $\overline { OA } =\left( x+4y \right) \overline { a } +\left( 2x+y+1 \right) \overline { b } ,\overline { OB } =\left( y-2x+2 \right) \overline { a } +\left( 2x-3y-1 \right) \overline { b }$ and $3\overline { OA } =2\overline { OB }, $ then $\left( x,y \right) =$

Question 10 :
Given $\vec p= (2,-4,1), \vec q = (3,-1,2), \vec r = (5,5, 4)$. Then $\vec{PQ}$ and $\vec{QR}$ are

Question 11 :
If $\vec {a}$ and $\vec {b}$ are non zero vectors such that $|\vec {a} + \vec {b}| = |\vec {a} - 2\vec {b}|$, then

Question 12 :
For which values of '$a$' the different vectors $ \overline { x } =\left( 2a,3a,0 \right) $ and $\overline { y } =\left( 0,0,4a \right) $ are orthogonal vectors

Question 13 :
lf $\overline{a},\overline{b},\ \overline{c}$ are three non-zero and non-null vectors and $\overline{r}$ is any vector in space, then $[\overline{b}\overline{c}\overline{r}]\overline{a}+[\overline{c}\overline{a}\overline{r}]\overline{b}+[\overline{a}\overline{b}\overline{r}]\overline{c}$ is equal to

Question 14 :
If $p$ , $q$ and $r$ are three non-coplanar vectors such that $p + q + r = \alpha s$ and $q + r + s = \beta p $. then $ p +q +r +s $ is equal to

Question 15 :
If a, b, c are position vectors of the vertices of a $\displaystyle \Delta ABC,$ then $ \displaystyle \overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}=$

Question 16 :
If the sum of two unit vectors is also a unit vector, then the angle between the two vectors is

Question 17 :
If $\bar{u}, \bar{v}, \bar{w}$ are non-coplanar vectors and p,q are real numbers, then the equality  $[3 \bar{u} \, p\bar{v} \, p \bar{w}] - [p\bar{v} \, \bar{w} \, q\bar{u}] - [2 \bar{w} \, q \bar{v} \,  q\bar{u}] = 0$ hold for

Question 19 :
If $\vec a,\ \vec b$ and $\vec c$ are three unit vectors, then $|\vec a-\vec b|^{2}+|\vec b-\vec c|^{2}+|\vec c-\vec a|^{2}$ does not exceed

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