2. Relative to a fixed origin \(O\),
the point \(A\) has position vector \(( 3 \mathbf { i } - \mathbf { j } + 2 \mathbf { k } )\)
the point \(B\) has position vector ( \(\mathbf { i } + 2 \mathbf { j } - 4 \mathbf { k }\) )
and the point \(C\) has position vector \(( - \mathbf { i } + \mathbf { j } + a \mathbf { k } )\), where \(a\) is a constant and \(a > 0\).
Given that \(| \overrightarrow { B C } | = \sqrt { 41 }\)
a. show that \(a = 2\).
\(D\) is the point such that \(A B C D\) forms a parallelogram.
b. Find the position vector of \(D\).