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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
Options
(a) λ = 1
(b) λ = −1
(c) a = |λ|
(d) \[a = \frac{1}{\left| \lambda \right|}\]
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Solution
(d) \[a = \frac{1}{\left| \lambda \right|}\]
\[\text{ Given that }\]
\[\left| \vec{a} \right| = a; \]
\[\text{ Now },\]
\[\left| \lambda \vec{a} \right| = 1\]
\[ \Rightarrow \left| \lambda \right| \left| \vec{a} \right| = 1\]
\[ \Rightarrow \left| \lambda \right|a = 1\]
\[ \Rightarrow a = \frac{1}{\left| \lambda \right|}\]
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