IB skill practice

Prove geometric results with vectors

Use vectors to prove parallelism, perpendicularity, collinearity, and midpoint results.

Paper 1, Paper 2 5 marks Difficulty 3

Prove geometric results with vectors - visual substitution line

In a parallelogram proof, \(|\mathbf{a}|=7\), \(|\mathbf{b}|=9\), and \(\mathbf{a}\cdot\mathbf{b}=12\). Enter \(|\mathbf{a}+\mathbf{b}|^{2}\).

Worked practice: result and interpretation

Calculate the requested result first, then choose the interpretation that follows from it.