Vector Algebra ...

Position vectors of mid point of the vector joining the points $$P(2, 3, 4)$$ and $$Q (4, 1, -2)$$ is

The projection $$\displaystyle 2\hat{i}+3\hat{j}-2\hat{k}$$ on the vector $$\displaystyle \hat{i}+2\hat{j}-3\hat{k}$$ is

$$\vec{A} \ and \ \vec{B}$$ are two vectors, find the angle between them, if
$$\left | \vec{A}\times \vec{B} \right |=\sqrt{3}(\vec{A.}\vec{B})$$ the value of is :-

Let $$\vec{AB}= 3\widehat {i} + \widehat{j}- \widehat{k}$$ and $$\vec{AC}=\widehat{i} -\widehat{j} +3\widehat{k}$$ and a point P on the line segment BC is equidistant from $$AB$$ and $$AC$$, then $$\vec{AP}$$ is 

The vector sum of (N) coplanar forces, each of magnitude F, when each force is making an angle of
$$\frac{2\pi }{N}$$ with that preceding one, is :

Four point charges $${q}_A=2\mu C$$, $${q}_B=5\mu C$$, $${q}_C=2\mu C$$, $${q}_D=5\mu C$$ are located at the four corners of a square ABCD of side 10 cm. The force on a charge of $$1\mu C$$ placed at the centre of the square is

If $$\vec{a}=3\hat{i}-2\hat{j}+\hat{k},\vec{b}=2\hat{i}-4\hat{j}-3\hat{k}$$, $$\vec{c}=-1\hat{i}+2\hat{j}+2\hat{k}$$ then $$\vec{a}+\vec{b}+\vec{c}=$$

Namita walks 14 metres towards west, then turns to her right and walks 14 metres and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance (in metres) between her starting point and the present position ?

The projection of $$\displaystyle a=3i-j+5k$$ on $$\displaystyle b=2i+3j+k$$ is

For $$O$$ being the origin and $$3$$ points $$P,Q$$ and $$R$$ lie on a plane. If $$\displaystyle \vec{PO}+\vec{OQ}=\vec{QO}+\vec{OR}$$, then $$P, Q, R$$ are