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1.10 Vectors

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Question 58

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.

a.

Determine the size of the interior angle PQRPQRPQR, giving your answer in degrees to 2 decimal places.

[4]
b.

Calculate the total surface area of the solar sail component PQRSPQRSPQRS, giving your answer to one decimal place.

[3]
Markscheme

1.10 Vectors Questions

  1. A Level
  2. /Maths
  3. /1.10 Vectors

197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.

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