Mathematics

Problem

Let

\vec{p}=3\mathbf{i}+k\mathbf{j}+4\mathbf{k}

and

\vec{q}=3\mathbf{i}-k\mathbf{j}+4\mathbf{k}

, where

k\neq 0

. Which of the following is always true about their magnitudes? a)

|\vec{p}|>|\vec{q}|

for every

k\,(\neq 0)

|\vec{p}|=|\vec{q}|

only when

k=0

|\vec{p}|=|\vec{q}|

|\vec{p}|>|\vec{q}|

\, if

k>0

and

|\vec{p}|<|\vec{q}|

\, if

k<0