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.
168 exam-style questions on OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.