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