The points PPP, QQQ, R R\,R and S S\,S have position vectors p=−5i+7j−4k\mathbf{p} = -5\mathbf{i} + 7\mathbf{j} - 4\mathbf{k}p=−5i+7j−4k, q=7i−2j+2k\mathbf{q} = 7\mathbf{i} - 2\mathbf{j} + 2\mathbf{k}q=7i−2j+2k, r=i−6j+3k\mathbf{r} = \mathbf{i} - 6\mathbf{j} + 3\mathbf{k}r=i−6j+3k and s=17i−18j+11k\mathbf{s} = 17\mathbf{i} - 18\mathbf{j} + 11\mathbf{k}s=17i−18j+11k
Show that PQ⃗\vec{PQ}PQ is parallel to RS⃗\vec{RS}RS, giving your answer in the form PQ⃗=λRS⃗\vec{PQ}=\lambda\vec{RS}PQ=λRS, where λ \lambda\,λ is an exact fraction.
309 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.