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  • A unit vector is represented as <img alt="\[(0.8\hat{i}+b\hat{j}+0.4\hat{k})\]" src="https://entrancecorner.oncodecogs.com/gif.latex?%5C%5B%280.8%5Chat%7Bi%7D&plus;b%5Chat%7Bj%7D&

A unit vector is represented as \[(0.8\hat{i}+b\hat{j}+0.4\hat{k})\]

. Hence the value of ‘b’ must be

Option: 1

0.4


Option: 2

\sqrt{0.6}


Option: 3

0.2


Option: 4

\sqrt{0.2}


Answers (1)

best_answer

For unit vector,

\left| 0.8\hat{i}+b\hat{j}+0.4\hat{k} \right|=1\

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

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

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

Squaring both sides we get, 

0.8+{{b}^{2}}=1 \\ {{b}^{2}}=1-0.8 \\ {{b}^{2}}=0.2 \\ b=\sqrt{0.2} \\

 

 

Posted by

sudhir.kumar

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