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

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

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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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