Two non-zero vectors a\mathbf{a}a and b\mathbf{b}b are such that ∣a+b∣=∣a∣+∣b∣|\mathbf{a} + \mathbf{b}| = |\mathbf{a}| + |\mathbf{b}|∣a+b∣=∣a∣+∣b∣ Explain the geometrical significance of this statement.
Two different vectors m\mathbf{m}m and n\mathbf{n}n are such that ∣m∣=5|\mathbf{m}| = 5∣m∣=5 and ∣m+n∣=7|\mathbf{m} + \mathbf{n}| = 7∣m+n∣=7. The angle between m\mathbf{m}m and n\mathbf{n}n is 30°30°30°. Find the angle between m\mathbf{m}m and m−n\mathbf{m} - \mathbf{n}m−n, giving your answer in degrees to 1 decimal place.
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.