The point A A\,A has the position vector (ab4)\begin{pmatrix} a \\ b \\ 4 \end{pmatrix}ab4 where a a\,a and b b\,b are positive constants, point B B\,B has the position vector (345)\begin{pmatrix} 3 \\ 4 \\ 5 \end{pmatrix}345 and point C C\,C has the position vector (123)\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}123. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Given that a+b=5a+b=5a+b=5 and the area of ABC ABC\,ABC is 333\sqrt{3}33, find the exact values of a a\,a and bbb.
309 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.