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.