The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If $\overrightarrow{Q}$ is doubled,the new resultant is perpendicular to $\overrightarrow{P}$. Then $R$ equals

If $\overrightarrow{ F }=2 \hat{ i }+\hat{ j }-\hat{ k }$ and $\overrightarrow{ r }=3 \hat{ i }+2 \hat{ j }-2 \hat{ k }$,then the scalar and vector products of $\overrightarrow{ F }$ and $\overrightarrow{ r }$ have the magnitudes respectively as

Given that $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$ and that $\overrightarrow{C}$ is $\perp$ to $\overrightarrow{A}$. Further,if $|\overrightarrow{A}| = |\overrightarrow{C}|$,then what is the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?

$100$ coplanar forces,each equal to $10 \ N$,act on a body. Each force makes an angle of $\pi/50$ radians with the preceding force. What is the resultant of the forces in $N$?

The three vectors $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}$,$\vec{B}=\hat{i}-3 \hat{j}+5 \hat{k}$ and $\vec{C}=2 \hat{i}-\hat{j}+4 \hat{k}$ will form

Two particles are located at an equal distance from the origin. The position vectors of these are represented by $\overrightarrow{A} = 2\hat{i} + 3n\hat{j} + 2\hat{k}$ and $\overrightarrow{B} = 2\hat{i} - 2\hat{j} + 4p\hat{k}$,respectively. If both vectors are at a right angle to each other,the value of $n^{-1}$ is . . . . . . .