The point A A\,A has the position vector (ab2)\begin{pmatrix} a \\ b \\ 2 \end{pmatrix}ab2 where a a\,a and b b\,b are positive constants, point B B\,B has the position vector (143)\begin{pmatrix} 1 \\ 4 \\ 3 \end{pmatrix}143 and point C C\,C has the position vector (361)\begin{pmatrix} 3 \\ 6 \\ 1 \end{pmatrix}361. ABC ABC\,ABC is an isosceles triangle with AB=ACAB = ACAB=AC.
Show that a+b=7a + b = 7a+b=7
Given that the area of ABC ABC\,ABC is 262\sqrt{6}26, 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.