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 (234)\begin{pmatrix} 2 \\ 3 \\ 4 \end{pmatrix}234 and point C C\,C has the position vector (012)\begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix}012. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Show that a+b=3a + b = 3a+b=3
Given that the area of ABC ABC\,ABC is 8\sqrt{8}8, find the exact values of a a\,a and bbb.
Practise Edexcel A Level Maths Vectors with exam-style questions for A Level Maths. 123 questions covering 11.1 Vectors, 11.2 Representing Vectors, 11.3 Magnitude and Direction, 11.4 Position Vectors, 11.5 Solving Geometric Problems, and 11.6 Modelling with Vectors, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
