If $\vec{a}=(p, -2, 5)$ and $\vec{b}=(1, q, -3)$ are collinear vectors,then:

If $\vec{a}$ and $\vec{b}$ are the position vectors of $A$ and $B$,respectively,find the position vector of a point $C$ in $BA$ produced such that $BC = 1.5 BA$.

If two vertices of a triangle are $\hat{i} - \hat{j}$ and $\hat{j} + \hat{k}$,then the third vertex can be

$D, E, F$ are points on the sides $BC, CA$ and $AB$ of a $\triangle ABC$ respectively,dividing them in the ratios $2:3, 1:2, 3:1$ internally. The lines $BE$ and $CF$ intersect on the line $AD$ at $P$. If $\overrightarrow{AP} = x_1 \overrightarrow{AB} + y_1 \overrightarrow{AC}$,then $x_1 + y_1 =$

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is

If $ABCD$ is a parallelogram with $AC$ and $BD$ as diagonals,then which of the following is true regarding the vector relationship between the diagonals and sides?