3. Relative to a fixed origin,
- point \(A\) has position vector \(- 2 \mathbf { i } + 4 \mathbf { j } + 7 \mathbf { k }\)
- point \(B\) has position vector \(- \mathbf { i } + 3 \mathbf { j } + 8 \mathbf { k }\)
- point \(C\) has position vector \(\mathbf { i } + \mathbf { j } + 4 \mathbf { k }\)
- point \(D\) has position vector \(- \mathbf { i } + 3 \mathbf { j } + 2 \mathbf { k }\)
a. Show that \(\overrightarrow { A B }\) and \(\overrightarrow { C D }\) are parallel and the ratio \(\overrightarrow { A B } : \overrightarrow { C D }\) in its simplest form.
b. Hence describe the quadrilateral \(A B C D\).