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If \(\overrightarrow a\) is a nonzero vector of magnitude $" a "$ and \(λ\) a nonzero scalar, then \(λ\) \(\overrightarrow a\) is unit vector if

\[ \begin{array} (A)\; λ = 1 \quad & (B)\; λ = -1 \quad & (C)\; a = |\; λ\; | \quad & (D)\; a = 1/|\; λ\; | \end{array} \]

1 Answer

  • A vector is said to be unit vector if its magnitude is 1.
Step 1:
Given :$\overrightarrow a$ is a non-zero vector of magnitude "a"
(i.e) $\mid\overrightarrow a=a$.
$|\lambda\overrightarrow a|=1$ is a unit vector if $|\lambda\overrightarrow a|=1$ or $|\lambda||\overrightarrow a|=1$
Step 2:
But $|\overrightarrow a|=a$
Hence $|\lambda|a=1$
$\Rightarrow a=\large\frac{1}{|\lambda|}$
Hence (D) is the correct option.
answered May 21, 2013 by sreemathi.v

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