Question 1 :
In Polygon Law of Vector Addition, the head of first vector is joined to the tail of last vector.
Question 2 :
$\mathrm{If}$ $\vec{AD},\ \vec{BE},\ \vec{CF}$ are medians of an equilateral triangle $\mathrm{A}\mathrm{B}\mathrm{C}$, then $\vec{AD}+\vec{BE}+\vec{CF}$ equals to <br/>
Question 3 :
The vector $z = 3 - 4i$ is turned anticlockwise through an angle of $180^{\circ}$ and stretched $\dfrac{5}{2}$ times. The complex number corresponding to the newly obtained vector is ....
Question 4 :
Direction angle of a vector is $30^{o}$, then find the vector.
Question 5 :
When a body is thrown up, the sign of $g$ is positive when it goes up.
Question 6 :
Given that $\vec{ A } \times \vec{ B } =\vec{ B } \times \vec { C } =\vec { 0 } $ if $\vec{ A } \vec { B } \vec { C } $ are not null vectors, Find the value of $\vec{ A } \times \vec{ C } $
Question 7 :
Let $a=\hat{i}+2\hat j+3\hat k$ and $b=3\hat i+\hat j$. Find the unit vector in the direction of the $a+b$.
Question 8 :
$\vec{a},\vec{b},\vec{c}$ are three non-collinear vectors such that $\vec{a}+\vec{b}$ is parallel to $\vec{c}$ and $\vec{a}+\vec{c}$ is parallel to $\vec{b}$ then:
Question 9 :
If a line has direction ratios $2,-1,-2$, determine its direction cosines.
Question 10 :
For non zero vectors $a,b$ and $c$, if $a+b+c=0$ then which relation true:-
Question 11 :
The vectors $\hat { i } +2\hat { j } +3\hat { k }$, $2\hat { i } -\hat { j } +\hat { k }$ and $3\hat { i } +\hat { j } +4\hat { k }$ are so placed that the end point of one vector is the starting point of the next vector. Then the vectors are :
Question 12 :
If the points $A$ and $B$ are $\left( 1,2,-1 \right)$ and $\left( 2,1,-1 \right)$ respectively, then $\vec { AB } $ is
Question 14 :
Express $ \vec{AB}$ in terms of unit vectors $ \hat{i} $ and $\hat{j}$, when the points are:<br>A(4,-1), B(1,3)<br>Find $ \left | \vec{AB} \right |$ in each case.
Question 15 :
For three vectors $\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}$ which of the following expressions is not equal to any of remaining is
Question 16 :
Find a vectorin which two of the three direction angles are $\alpha=75^{o}$ and $\beta=55^{o}$.
Question 17 :
Two vectors $a$ and $b$ are said to be equal, if<br>I. $|a| = |b|$<br>II. they have same or parallel support.<br>III. the same sense.<br>Which of the following is true?
Question 18 :
If $\cos \alpha, \cos \beta$ and $\cos \gamma$ are direction cosines of a vector, then they satisfy which of the following ? Prove it.
Question 20 :
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 21 :
If $\lambda (2\overline {i} - 4\overline {j} + 4\overline {k})$ is a unit vector then $\lambda =$
Question 22 :
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 23 :
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<br/>
Question 25 :
The position vectors of the points A,B,C are $\overline { i } + 2 \overline { j } - \overline { k } , \overline { i } + \overline { j } + \overline { k } , 2 \overline { i } + 3 \overline { j } + 2 \overline { k }$ respectively. If A is chosen as the origin then the position vectors of B and C are
Question 26 :
Let $\hat {a}$ and $\hat {b}$ two unit vector such that ${ \left( \hat { a } .\hat { b } \right) }^{ 2 }-\left| \hat { a } \times \hat { b } \right| $ is maximum then $\left| \hat { a } .\hat { b } \right|$ is equal to
Question 27 :
If $\vec {a}$ and $\vec {b}$ are unit vectors, then angle between $\vec {a}$ and $\vec {b}$ for $\sqrt {3} \vec {a} - \vec {b}$ to be unit vector is
Question 28 :
If $\vec a = \widehat i + 2 \hat j + 3\hat k, \vec b = 2 \hat i + 3 \hat j + \hat k, \vec c = 3 \hat i + \hat j + 2 \hat k$ are vectors satisfying<br/>$\alpha\vec a  + \beta \vec b + \gamma \vec c = - 3 (\hat i - \hat k)$, then the ordered triplet $(\alpha, \beta, \gamma)$ is
Question 29 :
If $\vec {a}$ and $\vec {b}$ are non zero vectors such that $|\vec {a} + \vec {b}| = |\vec {a} - 2\vec {b}|$, then
Question 30 :
If $a=\hat{i}+\hat{j}, b=2\hat{j}-\hat{k}$ and $r\times a=b\times a, r\times b=a\times b$, then a unit vector in the direction of ${r}$ is?
Question 32 :
If $A,B,C,D$ be any four points and $E$ and $F$ be the mid-points of $AC$ and $BD$, respectively, then $\vec{AB}+\vec{CB}+\vec{CD}+\vec{AD}$ is equal to
Question 33 :
Find the values of $x$ ,$y$ and $z$ so that the vectors $\overrightarrow { a } =x\hat { i } + 2\hat { j} +z\hat { k}$ and $\overrightarrow { b } =2\hat { i } + y\hat { j} +\hat { k}$ are equal
Question 34 :
If $\vec { a }$and $\vec { b }$  are not perpendicular and $\vec { c }$ and $\vec {d} $ are such that $\overrightarrow b  \times \overrightarrow c  = \overrightarrow b  \times \overrightarrow a \,\,and\,\,\,\overrightarrow a .\overrightarrow d  = 0$ then $\vec {d}$ is equal to- 
Question 35 :
Let P, Q, R and S be the points on the plane with position vectors $-2\hat{i}-\hat{j}, 4\hat{i}, 3\hat{i}+3\hat{j}$ and $-3\hat{i}+2\hat{j}$ respectively. the quadrilateral PQRS must be a.
Question 36 :
If three vectors $ a, b, c $ satisfy $ a+b+c=0$ and $ |a| = 3, |b| = 5, |c| = 7 , $ then the angle between $a$ and $b$ is :
Question 37 :
Let $A,B,C$ be distinct point with position vectors $\hat{i}+\hat{j}$, $\hat{i}-\hat{j}$, $p\hat{i}-q\hat{j}+r\hat{k}$ respectively. Points $A,B,C$ are collinear, then which of the following can be correct:
Question 38 :
Assertion: $\displaystyle\left ( A \right ): \overline{GA} +\overline{GB}+\overline{GC}=\bar{0}$ where $G$ is the centroid of triangle ABC.
Reason: $\displaystyle\left ( R \right ): \overline{AB}=$ P.V of $B-$ P.V of $A.$
Question 39 :
Assertion: $\vec{a} = 3 \vec{i} + p \vec{j} + 3 \vec{k}$ and $\vec{b} = 2 \vec{i} + 3 \vec{j } + q\vec{k}$ are parallel vectors if $p = \dfrac{9}{2}$ and $q = 2$.
Reason: If $\vec{a}= a_1 \vec{i} + a_2 \vec{j} + a_3 \vec{k}$ and $\vec{b} = b_1 \vec{i} + b_2 \vec{j} + b_3 \vec{k}$ are parallel, then $\displaystyle \dfrac{a_1}{b_1} = \dfrac{a_2}{b_2} = \dfrac{a_3}{b_3}$
Question 40 :
If  $\vec{e}=l\hat{i}+m \hat{j}+n\hat{k}$  is a unit vector, then the maximum value of  $lm+mn+nl$ is<br/>
Question 41 :
If $|a|=5.|\vec{b}|=4$, and $|c|=3$. then what will be the value of $\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}$ given that $\vec{a}+\vec{b}+\vec{c}=0$
Question 42 :
The value of $\vec i \times (\vec a \times \vec i) + \vec j \times (\vec a \times \vec j) + \vec k \times (\vec a \times \vec k)$ is (where $\vec i, \vec j, \vec k$ are unit vectors)
Question 43 :
If $(x, y, z) \neq (0, 0, 0)$ and $(\hat i + \hat j + 3\hat k) x + (3\hat i - 3\hat j + \hat k) y+(-4\hat i + 5\hat j) z = \lambda (x\hat  i +y\hat j +z\hat k)$, then the value of $\lambda$ will be
Question 44 :
If $\vec a$ is a non-zero vector of modulus $a$ and $m$ is a non-zero scalar, then $m \vec a$ is a unit vector if
Question 45 :
If $\overline {e} = l\overline {i} + m\overline {j} + n\overline {k}$ is a unit vector, the maximum value of $lm + mn + nl$ is
Question 46 :
The value of $x$ if $x(\hat { i } +\hat { j } +\hat { k } )$ is a unit vector is
Question 47 :
If $\overline{a}$ and $\overline{b}$ are two vectors, such that $\overline{a}. \overline{b} < 0$ and $|\overline{a}.\overline{b}| = |\overline{a}\times \overline{b}|$, then angle between vector $\overline{a}$ and $\overline{b}$ is
Question 48 :
If $|\vec{a} + \vec{b}| < |\vec{b} - \vec{a}|$ then angle between $\vec{a} \, $and $\, \vec{b}$ is
Question 50 :
A system of vectors is said to be coplanar, if<br/>I. Their scalar triple product is zero.<br/>II. They are linearly dependent.<br/>Which of the following is true?
