If $a, b$ and $c$ are three non-collinear points and $ka + 2b + 3c$ is a point in the plane of $a, b$ and $c$, then $k =$

If the vectors $(2 \hat{\imath} - q \hat{\jmath} + 3 \hat{k})$ and $(4 \hat{\imath} - 5 \hat{\jmath} + 6 \hat{k})$ are collinear,then the value of $q$ is

The position vectors of the points $P$ and $Q$ are respectively $-2 \bar{i}-3 \bar{j}+\bar{k}$ and $3 \bar{i}+3 \bar{j}+2 \bar{k}$. The ratio in which the point having position vector $\frac{-9}{2} \bar{i}-6 \bar{j}+\frac{1}{2} \bar{k}$ divides the line segment joining $P$ and $Q$ is

If $r \cdot i = r \cdot j = r \cdot k$ and $|r| = 3$, then $r = $

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

If $a$ and $b$ are adjacent sides of a rhombus,then