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 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.