Parallel vectors

Remark — Parallel vectors

Two vectors are parallel when they have proportional components: $\vec u\parallel\vec v \iff \frac{u_1}{v_1}=\frac{u_2}{v_2}=\frac{u_3}{v_3}.$ In that case their vector product is zero: $\vec u\times\vec v = \vec 0$.

The test of proportionality of the components and the vanishing of the vector product are two equivalent ways of recognising parallelism.

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Topics: Analytic geometry in space
Concepts: Vector product · Vector
Skills: Analytic geometry