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

A unit vector is represented as (0.8 i+b j+0.4 k). Hence the valu…

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MCQ

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
✓
$\sqrt{0.2}$

✓

Answer

Correct option: D.

$\sqrt{0.2}$

(d) : For unit vector, $|0.8 \hat{i}+b \hat{j}+0.4 \hat{k}|=1$
$
\begin{aligned}
& \sqrt{(0.8)^2+(b)^2+(0.4)^2}=1 \\
& \sqrt{0.64+b^2+0.16}=1
\end{aligned}
$
$\begin{aligned} & \sqrt{0.80+b^2}=1 \\ & 0.8+b^2=1 \Rightarrow b^2=0.2 \Rightarrow b=\sqrt{0.2}\end{aligned}$

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