If $A(1, 0, 0)$,$B(0, 1, 0)$,and $C(0, 0, 1)$ are given,and $\vec{AB} = \vec{CX}$,then the point $X$ is:

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:

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

If one side of a square is represented by the vector $3i + 4j + 5k,$ then the area of the square is

If $\bar{a}, \bar{b}, \bar{c}$ are the position vectors of the points $A(1,3,0), B(2,5,0), C(4,2,0)$ respectively and $\bar{c}=t_{1} \bar{a}+t_{2} \bar{b}$,then the value of $t_{1} t_{2}$ is:

If a point $C$ divides the line segment joining the points with the position vectors $2 \hat{i}-3 \hat{j}+2 \hat{k}$ and $3 \hat{i}-\hat{j}-2 \hat{k}$ in the ratio $2: 3$,then the distance of $C$ from the point with position vector $2 \hat{i}-\hat{j}+\hat{k}$ is