If $O$ is the origin and the position vector of $A$ is $4\,i + 5\,j$,then a unit vector parallel to $\overrightarrow{OA}$ is:

$PQRS$ is a quadrilateral and $PQ=a, QR=b, SP=a-b$. $M$ is the mid-point of $QR$ and $X$ is a point on $SM$ such that $SX=\frac{4}{5}SM$. If $SM=m(4a-b)$ and $SX=n(4a-b)$,then $m+n=$

Let $u$ and $v$ be two vectors. Then $|u-v|=||u|-|v||$ if and only if

If $3 \hat{i}-5 \hat{j}+2 \hat{k}, 7 \hat{i}+2 \hat{j}-4 \hat{k}, \hat{i}-3 \hat{j}+4 \hat{k}$ and $-7 \hat{i}-17 \hat{j}+16 \hat{k}$ are position vectors of the points $A, B, C$ and $D$ respectively, then the angle between $\overrightarrow{AB}$ and $\overrightarrow{CD}$ is

Find the value of $x$ for which $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector.

Let $A(3 \hat{i}+\hat{j}-\hat{k})$ and $B(13 \hat{i}-4 \hat{j}+9 \hat{k})$ be two points on a line $L$. $C$ and $D$ are points on $L$ on either side of $A$ at distances of $9$ and $6$ units respectively, and $C$ lies between $A$ and $B$. Then the position vectors of $C$ and $D$ are respectively: