A unit vector is represented as ( 0.8 i ^ + b j ^ + 0.4 k ^ ) . Hence the value of 'b' must be

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A unit vector is represented as

(0.8 \hat{i} + b \hat{j} + 0.4 \hat{k})

. Hence the value of 'b' must be

PhysicsMathematics in PhysicsMHT CETMHT CET 2018

Options:

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

Solution:

2148 Upvotes Verified Answer

The correct answer is:

\sqrt{0.2}

\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}

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