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Further vectors formulae

The 3 results the further vectors notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 3, the formulae booklet prints 1 and 2 are yours to memorise.

Further Maths · 2 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

2 lessons

Lines and planes in three dimensions

r=a+λb\text{r} = \text{a} + λ\text{b}NOT IN THE BOOKLET: LEARN ITConditionsb ≠ 0, and a the position vector of a point on the line.
r·n=a·n=d\text{r} · \text{n} = \text{a} · \text{n} = dNOT IN THE BOOKLET: LEARN ITConditionsn a non-zero normal to the plane, a the position vector of a point on it.

Intersections, angles and distances

distance=|n1x0+n2y0+n3z0-d||n|\text{distance} = \frac{|n_{1}x_{0} + n_{2}y_{0} + n_{3}z_{0} - d|}{|\text{n}|}IN THE FORMULAE BOOKLETConditionsThe plane written as r·n = d with n = (n₁, n₂, n₃) and |n| ≠ 0. The booklet writes the plane as n₁x + n₂y + n₃z + d = 0, so its numerator has + d.

Every formula in the library is indexed by unit on the equation index, and the further vectors notes are where these results are derived and used. The 2 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Further algebra and series formulae · Further calculus formulae