The point A A\,A has the position vector (ab3)\begin{pmatrix} a \\ b \\ 3 \end{pmatrix}ab3 where a a\,a and b b\,b are positive constants, point B B\,B has the position vector (114)\begin{pmatrix} 1 \\ 1 \\ 4 \end{pmatrix}114 and point C C\,C has the position vector (772)\begin{pmatrix} 7 \\ 7 \\ 2 \end{pmatrix}772. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Show that a+b=8a + b = 8a+b=8
Given that the area of ABC ABC\,ABC is 114\sqrt{114}114, 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.