Relative to a fixed origin OOO, the points AAA, B B\,B and C C\,C have position vectors
a=i+j+k\mathbf{a} = \mathbf{i} + \mathbf{j} + \mathbf{k}a=i+j+k, b=3i+3k\mathbf{b} = 3\mathbf{i} + 3\mathbf{k}b=3i+3k, c=2i+3j+3k\mathbf{c} = 2\mathbf{i} + 3\mathbf{j} + 3\mathbf{k}c=2i+3j+3k
Show that the triangle ABC ABC\,ABC is isosceles.
Find the exact area of the triangle ABCABCABC.
168 exam-style questions on AQA A Level Maths 1.13 J: Vectors, covering 1.13.1 Vectors in two and three dimensions, 1.13.2 Magnitude and direction of a vector, 1.13.3 Vector arithmetic, 1.13.4 Position vectors, and 1.13.5 Vectors to solve problems. Each one has a worked solution and a mark scheme showing where the marks go.