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+5k\mathbf{c} = -\mathbf{i} + 4\mathbf{j} + 5\mathbf{k}c=−i+4j+5k
Find ∣AB⃗∣\left|\vec{AB}\right|AB and ∣AC⃗∣\left|\vec{AC}\right|AC, giving each answer in exact form.
The point D D\,D is such that ABDC ABDC\,ABDC is a parallelogram. Find the position vector of DDD.
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.