The position vector of a point $C$ with respect to $B$ is $i + j$ and that of $B$ with respect to $A$ is $i - j$. The position vector of $C$ with respect to $A$ is

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

The direction cosines of the vector $\hat{i}-2\hat{j}+3\hat{k}$ are . . . . . . .

Let the three sides of a triangle $ABC$ be represented by the vectors $\vec{AB} = 2\hat{i}-\hat{j}+\hat{k}$,$\vec{BC} = 3\hat{i}-4\hat{j}-4\hat{k}$,and $\vec{CA} = \hat{i}-3\hat{j}-5\hat{k}$. Let $G$ be the centroid of the triangle $ABC$. Then $6(|\overrightarrow{AG}|^2+|\overrightarrow{BG}|^2+|\overrightarrow{CG}|^2)$ is equal to

The position vectors of $A$ and $B$ are $2i - 9j - 4k$ and $6i - 3j + 8k$ respectively. Then the magnitude of $\overrightarrow{AB}$ is:

In a triangle $ABC$,if $2\overrightarrow{AC} = 3\overrightarrow{CB}$,then $2\overrightarrow{OA} + 3\overrightarrow{OB}$ equals