13. Relative to a fixed origin \(O\)
- the point \(P\) has position vector \(( 0 , - 1,2 )\)
- the point \(Q\) has position vector \(( 1,1,5 )\)
- the point \(R\) has position vector ( \(3,5 , m\) )
where \(m\) is a constant.
Given that \(P , Q\) and \(R\) lie on a straight line,
a. find the value of \(m\)
The line segment \(O Q\) is extended to a point \(T\) so that \(\overrightarrow { R T }\) is parallel to \(\overrightarrow { O P }\)
b. Show that \(| \overrightarrow { O T } | = 9 \sqrt { 3 }\).