Question

Write two different vectors having same magnitude.

Answer 1

Consider $\vec a$ $= (\hat i-2\hat j+3\hat k)$ and $\vec b$ =$(2\hat i+\hat j-3\hat k)$.

It can be observed that:

$|\vec a|$= $\sqrt {1^2+(-2)^2+3^2}$ = $\sqrt {1+4+9}$ = $\sqrt {14}$

$|\vec b|$ = $\sqrt {2^2+1^2+(-3)^2}$ = $\sqrt {4+1+9}$ = $\sqrt {14}$

Hence, $\vec a$ and $\vec b$ are two different vectors having the same magnitude. The vectors are different because they have different directions.