Review question

# Can we find the angle between the planes $ABC$ and $ABD$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6449

## Question

The position vectors of four points $A$, $B$, $C$, $D$ relative to an origin $O$ are given below. The vectors $\mathbf{i}$, $\mathbf{j}$, $\mathbf{k}$ are mutually perpendicular unit vectors. \begin{align*} A \colon\;& 2\mathbf{i} + 3\mathbf{j} + \mathbf{k}, \\ B \colon\;& \phantom{2}\mathbf{i} + \phantom{3}\mathbf{j} - \mathbf{k}, \\ C \colon\;& \phantom{2}\mathbf{i} \phantom{{}+{}3\mathbf{i}} + \mathbf{k}, \\ D \colon\;& \phantom{2\mathbf{i}{}+{}} 3\mathbf{j}.\phantom{{}+{}\mathbf{k}} \end{align*}

Find

1. the equation (in any form) of the line $AB$,
2. the shortest distance between $AB$ and $CD$,
3. the equation (in any form) of the plane $ABC$,
4. the angle between the planes $ABC$ and $ABD$.