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,
\[\left| m \overrightarrow{a} \right| = 1\]
\[ \Rightarrow \left| m \right| \left| \overrightarrow{a} \right| = 1\]
\[ \Rightarrow \left| m \right| a = 1\]
\[ \Rightarrow \left| m \right| = \frac{1}{a}\]
\[ \Rightarrow m = \pm \frac{1}{a}\]