If a- is a nonzero vector of magnitude -a- and - a nonzero scalar- then -a- is unit vector if

The correct option is D a=1|λ| Vector λa⃗ is a unit vector if |λa⃗|=1 .Now, |λa⃗|=1 ⇒ |λ||a⃗|=1 ⇒ |a⃗|=1|λ|, [λ≠ 0] ⇒ a=1| ...

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Byju's Answer

Standard XII

Physics

Intensity Amplitude Relationship

If a⃗ is a ...

Question

If $\to a$ is a nonzero vector of magnitude $^{'} a^{'}$ and $λ$ a nonzero scalar, then $λ \to a$ is unit vector if

λ = 1

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λ = - 1

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a = | λ |

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a = \frac{1}{| λ |}

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Solution

The correct option is D $a = \frac{1}{| λ |}$
Vector $λ \to a$ is a unit vector if $| λ \to a | = 1$ .
Now,
$| λ \to a | = 1$
$\Rightarrow | λ | | \to a | = 1$
$\Rightarrow | \to a | = \frac{1}{| λ |}, [λ \neq 0]$
$\Rightarrow a = \frac{1}{| λ |}, [∵ | \to a | = a]$
Hence, vector $λ \to a$ is a unit vector if $a = \frac{1}{| λ |}$
Thus the correct answer is $D$ .

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If $\to a$ is a nonzero vector of magnitude $^{'} a^{'}$ and $λ$ a nonzero scalar, then $λ \to a$ is unit vector if