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 

विकल्प

• (a) λ = 1 

• (b) λ = −1 

• (c) a = |λ| 

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

Answer 1

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

\[\text{ Given that }\]
\[\left| \vec{a} \right| = a; \]
\[\text{ Now },\]
\[\left| \lambda \vec{a} \right| = 1\]
\[ \Rightarrow \left| \lambda \right| \left| \vec{a} \right| = 1\]
\[ \Rightarrow \left| \lambda \right|a = 1\]
\[ \Rightarrow a = \frac{1}{\left| \lambda \right|}\]