4.
Relative to a fixed origin \(O\),
the point \(A\) has position vector \(( 2 \mathbf { i } + 3 \mathbf { j } - 4 \mathbf { k } )\),
the point \(B\) has position vector \(( 4 \mathbf { i } - 2 \mathbf { j } + 3 \mathbf { k } )\),
and the point \(C\) has position vector \(( a \mathbf { i } + 5 \mathbf { j } - 2 \mathbf { k } )\), where \(a\) is a constant and \(a < 0\)
\(D\) is the point such that \(\overrightarrow { A B } = \overrightarrow { B D }\).
- Find the position vector of \(D\).
(2)
Given \(| \overrightarrow { A C } | = 4\) - find the value of \(a\).
(3)