- Relative to a fixed origin \(O\)
- the point \(A\) has position vector \(5 \mathbf { i } + 3 \mathbf { j } + 2 \mathbf { k }\)
- the point \(B\) has position vector \(2 \mathbf { i } + 4 \mathbf { j } + a \mathbf { k }\)
where \(a\) is a positive integer.
- Show that \(| \overrightarrow { O A } | = \sqrt { 38 }\)
- Find the smallest value of \(a\) for which
$$| \overrightarrow { O B } | > | \overrightarrow { O A } |$$