Question 2 :
If $\lambda (2\overline {i} - 4\overline {j} + 4\overline {k})$ is a unit vector then $\lambda =$
Question 3 :
If $\cos \alpha, \cos \beta$ and $\cos \gamma$ are direction cosines of a vector, then they satisfy which of the following ? Prove it.
Question 8 :
State the following statement is True or False<br/>If the starting and end points of a vector are collinear, it is known as a unit vector.
Question 9 :
find the coordinate of the tip of the position vector which is equivalent to $ \vec{AB}$, where the coordinates of A and B are (-1, 3) and (-2, 1) respectively.
Question 10 :
Direction angle of a vector is $30^{o}$, then find the vector.
Question 11 :
For non zero vectors $a,b$ and $c$, if $a+b+c=0$ then which relation true:-
Question 13 :
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 :
For three vectors $\overrightarrow{u},\overrightarrow{v},\overrightarrow{w}$ which of the following expressions is not equal to any of remaining is
Question 15 :
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 17 :
Find the magnitude of two vectors $\vec a$ and $\vec b$, having the same magnitude and such that the angle between them is ${60^ \circ }$ and their scalar product is $\dfrac{1}{2}$.
Question 18 :
If the position vectors of the points $A(3,4),B(5, -6)$ and $C(4,-1)$ are $ \vec{a}, \vec{b}, \vec{c}$ respectively, compute $ \vec{a}+2\vec{b}-3\vec{c}. $<br/>
Question 19 :
If $|\overrightarrow{a}| = 5, |\overrightarrow{a} - \overrightarrow{b}|=8$ and $|\overrightarrow{a} + \overrightarrow{b}| = 10$, then $|\overrightarrow{b}|$ is equal to:
Question 21 :
If the position vectors of $P$ and $Q$ are $\overline{i}+2\overline{j}-7\overline{k}$ and $5\overline{i}-3\overline{j}+4\overline{k}$ respectively then the cosine of the angle between $\overline{PQ}$ and $z$-axis is<br/>
Question 22 :
If $a=i-j,b=i+j,c=i+3j+5k$ and $n$ is a unit vector such that $b,n=0,a,n=0$ then the value of $|c,n|$ is equal to
Question 23 :
Cosine of an angle between the vectors $\vec{a}+\vec{b}$ and $\vec{a}-\vec{b}$ if $|\vec{a}|=2, |\vec{b}|=1$ and $\vec{a}$ ^ $\vec{b}=60^o$ is?
Question 24 :
If the vectors $\hat i - \hat j, \hat j + \hat k$ and $\vec a$ form a triangle, then $\vec a$ may be
Question 26 :
A unit vector $d$ is equally inclined at an angle $\alpha$ with the vectors $a=\cos \theta. i+ \sin \theta. j , b=-\sin \theta.i+\cos =\theta. j$ and $c=k$. Then $\alpha$ is equal to 
