7．Relative to a fixed origin \(O\) the points \(A , B\) and \(C\) have position vectors $$\mathbf { a } = - \mathbf { i } + \frac { 4 } { 3 } \mathbf { j } + 7 \mathbf { k } , \quad \mathbf { b } = 4 \mathbf { i } + \frac { 4 } { 3 } \mathbf { j } + 2 \mathbf { k } \text { and } \mathbf { c } = 6 \mathbf { i } + \frac { 16 } { 3 } \mathbf { j } + 2 \mathbf { k } \text { respectively. }$$ （a）Find the cosine of angle \(A B C\) ． The quadrilateral \(A B C D\) is a kite \(K\) ．
（b）Find the area of \(K\) ． A circle is drawn inside \(K\) so that it touches each of the 4 sides of \(K\) ．
（c）Find the radius of the circle，giving your answer in the form \(p \sqrt { } ( q ) - q \sqrt { } ( p )\) ，where \(p\) and \(q\) are positive integers．
（d）Find the position vector of the point \(D\) ．
（Total 18 marks）