Question

If $\overrightarrow{a}$is a non-zero vector of magnitude 'a' and λ is a non-zero scalar, then λ$\overrightarrow{a}$ is a unit vector if
(a) λ = 1
(b) λ = −1
(c) a = |λ|
(d) $a=\frac{1}{\left|\lambda \right|}$

Answer 1

(d) $a=\frac{1}{\left|\lambda \right|}$

$$\begin{gathered} \text{Given that} \\ \left|\overrightarrow{a}\right|=a; \\ \text{Now,} \\ \left|\lambda \overrightarrow{a}\right|=1 \\ \Rightarrow \left|\lambda \right|\left|\overrightarrow{a}\right|=1 \\ \Rightarrow \left|\lambda \right|a=1 \\ \Rightarrow a=\frac{1}{\left|\lambda \right|} \end{gathered}$$