Mathematics

Problem

A vector

\vec{u}=k\mathbf{i}+k\mathbf{j}+k\mathbf{k}

is obtained by multiplying each component of

\vec{v}=\mathbf{i}+\mathbf{j}+\mathbf{k}

k>0

. Explain whether the magnitude of

\vec{u}

equals

k

times the magnitude of

\vec{v}