For a vector in

MATHEMATICS · Single correct · A Level · Mathematics · Vectors · Vectors

Problem

For a vector

\mathbf{a}

\mathbb{R}^3

, suppose

\mathbf{a}\cdot\mathbf{a}=0

. Which one of the following must be true? (a)

|\mathbf{a}|=1

(b) At least one component of

\mathbf{a}

equals

0

(c)

\mathbf{a}=\mathbf{0}

(d)

\mathbf{a}

is perpendicular to itself but

\mathbf{a}\neq\mathbf{0}