Question

If $\overrightarrow{a}$ is a non-zero vector of modulus a and m is a non-zero scalar such that m $\overrightarrow{a}$ is a unit vector, write the value of m.

Answer 1

Given $\overrightarrow{a}$ a non zero vector with modulus $a$. Also, $m\overrightarrow{a}$ is the unit vector. Therefore,
$$\begin{gathered} \left|m\overrightarrow{a}\right|=1 \\ \Rightarrow \left|m\right|\left|\overrightarrow{a}\right|=1 \\ \Rightarrow \left|m\right|a=1 \\ \Rightarrow \left|m\right|=\frac{1}{a} \\ \Rightarrow m=\pm \frac{1}{a} \end{gathered}$$