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. a+b=3a+b=3a+b=3.
Show that AB=ACAB = ACAB=AC
Given that a=3+233\displaystyle a = \frac{3+2\sqrt{3}}{3}a=33+23 and b=6−233\displaystyle b = \frac{6-2\sqrt{3}}{3}b=36−23, find the exact area of ABCABCABC.
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.