9709 P31 - Jun 2023 - Q6 - 10 marks
2178
Relative to origin \(O\), \(A=(2,1,3)\), \(B=(4,3,2)\), \(C=(3,-2,-4)\). \(ABCD\) is a parallelogram.
(a) Find the position vector of D. [3]
(b) The angle between \(BA\) and \(BC\) is \(\theta\). Find the exact value of \(\cos\theta\). [3]
(c) Hence find the area of \(ABCD\), in the form \(p\sqrt q\), with integer \(p,q\). [4]
