9709 P35 - Jun 2025 - Q10 - 8 marks
9533
The position vectors are \(\overrightarrow{OA}=2\mathbf i-\mathbf j-6\mathbf k\), \(\overrightarrow{OB}=b\mathbf i-2\mathbf j+3\mathbf k\), \(\overrightarrow{OC}=-4\mathbf i+5\mathbf j-2\mathbf k\).
(a) Given \(|\overrightarrow{AB}|=|\overrightarrow{BC}|\), find \(b\). [3]
(b) \(A,B,C,D\) are the vertices of a rhombus. Find the position vector of \(D\). [2]
(c) Calculate \(\angle ABC\). [3]
