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LearnAQA7367First teaching 2017Paper 2 · Compulsory contentFurther vectors

Paper 2 · Module

Further vectors

2 subtopics≈ 95 min in total

Start the module: Vector product and planes Open graphing calculator

Vector product and planes
$\mathbf a\times\mathbf b$ is a vector perpendicular to both $\mathbf a$ and $\mathbf b$ , of length $|\mathbf a||\mathbf b|\sin\theta$ . A plane is fixed by a point and a normal $\mathbf n$ : $\mathbf r\cdot\mathbf n=\mathbf a\cdot\mathbf n$ , or $ax+by+cz=d$ . Substituting a line into a plane finds where they meet.
≈ 50 min
Shortest distances and triple products
The shortest distance is always along a perpendicular. From point $P$ to plane $\mathbf r\cdot\mathbf n=d$ : $\frac{|\mathbf p\cdot\mathbf n-d|}{|\mathbf n|}$ . Between skew lines: project the join of two points onto $\mathbf n=\mathbf d_1\times\mathbf d_2$ . The triple product $\mathbf a\cdot(\mathbf b\times\mathbf c)$ is the volume of the parallelepiped.
≈ 45 min

AQA 7367 Further vectors — A Level Further Mathematics · Salam Academy