Q128 / 150 · MHT CET 2018 · Physics

A unit vector is represented as $(0.8 \hat{i} + b \hat{j} + 0.4 \hat{k})$ . Hence the value of 'b' must be

A
0.4
B
$\sqrt{0.6}$
C
0.2
Correct answer
D
$\sqrt{0.2}$

Solution

\sqrt{{(0.8)}^{2} + {(b)}^{2} + {(0.4)}^{2}} = 1

\sqrt{0.64 + b^{2} + 0.16} = 1

\sqrt{0.80 + b^{2}} = 1

0.80 + b^{2} = 1

b^{2} = 0.2

b = \sqrt{0.2}

Hence, the correct answer is option: 'D'.

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