MCQ
The unit vector along $\hat{i}+2 \hat{j}+\hat{k}$ will be :
- A$\hat{i}+2 \hat{j}+\hat{k}$
- B$\frac{\hat{i}+2 \hat{j}+\hat{k}}{3}$
- ✓$\frac{\hat{i}+2 \hat{j}+\hat{k}}{\sqrt{6}}$
- D$\sqrt{\hat{i}+2 \hat{j}+\hat{k}}$
✓
Answer
Correct option: C.
$\frac{\hat{i}+2 \hat{j}+\hat{k}}{\sqrt{6}}$
(C)
$\begin{aligned}
\text { Unit vector }= & \frac{\text { Vector }}{\text { Magnitude of vector }} \\
& =\frac{\hat{i}+2 \hat{j}+\hat{k}}{\sqrt{(1)^2+(2)^2+(1)^2}} \\
& =\frac{\hat{i}+2 \hat{j}+\hat{k}}{\sqrt{6}}
\end{aligned}
$
Hence, the correct option is (C).
$\begin{aligned}
\text { Unit vector }= & \frac{\text { Vector }}{\text { Magnitude of vector }} \\
& =\frac{\hat{i}+2 \hat{j}+\hat{k}}{\sqrt{(1)^2+(2)^2+(1)^2}} \\
& =\frac{\hat{i}+2 \hat{j}+\hat{k}}{\sqrt{6}}
\end{aligned}
$
Hence, the correct option is (C).
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