2 The points \(\mathrm { A } , \mathrm { B }\) and C have position vectors \(3 \mathbf { i } - 4 \mathbf { j } + 2 \mathbf { k } , - \mathbf { i } + 6 \mathbf { k }\) and \(7 \mathbf { i } - 4 \mathbf { j } - 2 \mathbf { k }\) respectively. M is the midpoint of BC .
- Show that the magnitude of \(\overrightarrow { O M }\) is equal to \(\sqrt { 17 }\).
Point D is such that \(\overrightarrow { B C } = \overrightarrow { A D }\).
- Show that position vector of the point D is \(11 \mathbf { i } - 8 \mathbf { j } - 6 \mathbf { k }\).