A specialized solar sail component is designed in the shape of a parallelogram PQRSPQRSPQRS. The positions of the vertices are measured relative to a central docking hub. The displacement vector from vertex P P\,P to vertex Q Q\,Q is given by PQ⃗=2i+10j−11k\vec{PQ} = 2\mathbf{i} + 10\mathbf{j} - 11\mathbf{k}PQ=2i+10j−11k and the displacement vector from vertex Q Q\,Q to R R\,R is given by QR⃗=−6i+3j+2k\vec{QR} = -6\mathbf{i} + 3\mathbf{j} + 2\mathbf{k}QR=−6i+3j+2k.
Determine the size of the interior angle PQRPQRPQR, giving your answer in degrees to 2 decimal places.
Calculate the total surface area of the solar sail component PQRSPQRSPQRS, giving your answer to one decimal place.
109 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.