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Question:
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If $\vec{a}$ is a non-zero vector of magnitude ' $a$ ' and $\lambda$ is a nonzero scalar, then $\lambda \vec{a}$ is unit vector if
(a) $\lambda=1$
(b) $\lambda=-1$
(c) $a=|\lambda|$
(d) $a=\frac{1}{|\lambda|}$.
(a) $\lambda=1$
(b) $\lambda=-1$
(c) $a=|\lambda|$
(d) $a=\frac{1}{|\lambda|}$.
Solution:
2808 Upvotes
Verified Answer
$$
|\vec{a}|=a
$$
Given: $\quad \lambda \vec{a}$ is a unit vector
$$
\begin{aligned}
&\Rightarrow|\lambda \vec{a}|=1 \quad \Rightarrow|\lambda||\vec{a}|=1 \\
&\Rightarrow|\lambda| a=1 \Rightarrow a=\frac{1}{|\lambda|}
\end{aligned}
$$
Hence option (d), is correct.
|\vec{a}|=a
$$
Given: $\quad \lambda \vec{a}$ is a unit vector
$$
\begin{aligned}
&\Rightarrow|\lambda \vec{a}|=1 \quad \Rightarrow|\lambda||\vec{a}|=1 \\
&\Rightarrow|\lambda| a=1 \Rightarrow a=\frac{1}{|\lambda|}
\end{aligned}
$$
Hence option (d), is correct.
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