#### Question

If \[\vec{a}\] is a non-zero vector of magnitude '*a*' and λ is a non-zero scalar, then λ \[\vec{a}\] is a unit vector if

(a) λ = 1

(b) λ = −1

(c)

*a*= |λ|(d) \[a = \frac{1}{\left| \lambda \right|}\]

#### Solution

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

\[\text{ Given that }\]

\[\left| \vec{a} \right| = a; \]

\[\text{ Now },\]

\[\left| \lambda \vec{a} \right| = 1\]

\[ \Rightarrow \left| \lambda \right| \left| \vec{a} \right| = 1\]

\[ \Rightarrow \left| \lambda \right|a = 1\]

\[ \Rightarrow a = \frac{1}{\left| \lambda \right|}\]

Is there an error in this question or solution?

Solution If → a is a Non-zero Vector of Magnitude 'A' and λ is a Non-zero Scalar, Then λ → a is a Unit Vector If Concept: Introduction of Vector.