The points AAA, B B\,B and C C\,C have position vectors
a=2i−j+3k\mathbf{a} = 2\mathbf{i} - \mathbf{j} + 3\mathbf{k}a=2i−j+3k, b=5i+2j−k\mathbf{b} = 5\mathbf{i} + 2\mathbf{j} - \mathbf{k}b=5i+2j−k, c=i+4j+3k\mathbf{c} = \mathbf{i} + 4\mathbf{j} + 3\mathbf{k}c=i+4j+3k
Find the position vector of the midpoint M M\,M of BCBCBC.
Find ∣AM⃗∣\left|\vec{AM}\right|AM, giving your answer in exact form.
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.