Given that $0.2$ $ˆ i + 0.6 ˆ j + a ˆ k$ is a unit vector, what is the value of $a$ ?

\sqrt{0.3}

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\sqrt{0.4}

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\sqrt{0.6}

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\sqrt{0.8}

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Solution

The correct option is B $\sqrt{0.6}$
We have, $0.2 ˆ i + 0.6 ˆ j + a ˆ k$ as a unit vector
$∴ | 0.2 ˆ i + 0.6 ˆ j + a ˆ k | = 1$
$∴ (0.2)^{2} + (0.6)^{2} + a^{2} = 1$
$∴ a = \sqrt{0.6}$

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