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 geometrically the significance of this statement.
Two different vectors, m\mathbf{m}m and n\mathbf{n}n, are such that ∣m∣=11|\mathbf{m}| = 11∣m∣=11 and ∣m+n∣=19|\mathbf{m} + \mathbf{n}| = 19∣m+n∣=19 The angle between vector m\mathbf{m}m and vector n\mathbf{n}n is 30∘30^{\circ}30∘
Find the angle between vector m\mathbf{m}m and vector m−n\mathbf{m} - \mathbf{n}m−n, giving your answer in degrees to one decimal place.
284 exam-style questions on Edexcel A Level Maths Vectors, covering 11.1 Vectors, 11.2 Representing Vectors, 11.3 Magnitude and Direction, 11.4 Position Vectors, 11.5 Solving Geometric Problems, and 11.6 Modelling with Vectors. Each one has a worked solution and a mark scheme showing where the marks go.