Worked examples

Vectors in the plane and in space

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Operations with components, magnitudes and unit vectors
• 2Angles between vectors with the dot product
• 3Orthogonal vectors and orthogonal projections
• 4Cross products and vectors orthogonal to two given vectors
• 5Areas of parallelograms and triangles
• 6Parallel vectors and collinear points
• 7Volumes and coplanarity with the scalar triple product