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.
Practise AQA A Level Maths 1.13 J: Vectors with exam-style questions for A Level Maths. 122 questions 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, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
