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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 - CBSE (Arts) Class 12 - Mathematics

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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?

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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.
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