The point A A\,A has position vector (ab3)\begin{pmatrix} a \\ b \\ 3 \end{pmatrix}ab3, where a a\,a and b b\,b are positive constants, the point B B\,B has position vector (234)\begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}234 and the point C C\,C has position vector (012)\begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix}012.
ABC ABC\,ABC is an isosceles triangle in which AB=ACAB = ACAB=AC.
Show that a+b=3a + b = 3a+b=3.
Given that the area of the triangle ABC ABC\,ABC is 8\sqrt{8}8, find the exact values of a a\,a and bbb.
197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.