Parallel & Perpendicular — Vectors (Mathematics)

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Pattern Recognition

Parallel vs Perpendicular

Two of the most common CSCA vector questions. Spot the keyword, apply the right test.

Parallel: \frac{a _{1}}{b _{1}} = \frac{a _{2}}{b _{2}} Perpendicular: a \cdot b = 0

Two different tests for two different keywords

Parallel

Components in ratio

$\frac{a _{1}}{b _{1}} = \frac{a _{2}}{b _{2}}$ (cross-multiply)

Perpendicular

Dot product = 0

$a \cdot b = 0$ (and neither is zero)

Angle

$cos θ = \frac{a \cdot b}{∣ a ∣∣ b ∣}$

Recover angle from dot product