Review question

# What is the position vector of $D$ if $ABCD$ is a parallelogram? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8215

## Question

The position vectors of points $A$, $B$ and $C$ are $\begin{equation*} \mathbf{a} = 4\mathbf{i} - 9\mathbf{j} - \mathbf{k}, \quad \mathbf{b} = \mathbf{i} + 3\mathbf{j} + 5\mathbf{k}, \quad\text{and}\quad \mathbf{c} = p\mathbf{i} - \mathbf{j} + 3\mathbf{k}. \end{equation*}$
1. Find the unit vector parallel to the vector $\mathbf{AB}$.
2. Find the value of $p$ such that $A$, $B$ and $C$ are collinear.
3. If $p = -2$, find the position vector of $D$ so that $ABCD$ is a parallelogram.