Vectors in 3 Dimensions (AQA A-Level Mathematics): Flashcards

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Vectors in 3 Dimensions
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Magnitude of a vector (definition)

Its length

Magnitude formula for 3D vector

∣a∣=x2+y2+z2|\mathbf{a}| = \sqrt{x^2 + y^2 + z^2}

AB→\overrightarrow{AB} from position vectors A and B

B−A\mathbf{B} - \mathbf{A}

Unit vector (definition)

A vector of length 1

Finding unit vector from a\mathbf{a}

Divide a\mathbf{a} by ∣a∣|\mathbf{a}|

Term used in 3D instead of gradient

Direction

Parallel vectors in 3D

They have the same direction

Mathematical relationship of parallel vectors

One is a scalar multiple of the other

First step: distance between position vectors

Find the vector between them

After finding AB→\overrightarrow{AB}, distance is...

∣AB→∣|\overrightarrow{AB}|

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