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Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
MCQ
The unit vector along the vector $\vec{a}=-2 \hat{i}+3 \hat{j}-\hat{k}$ is :
  • A
    $\frac{2 \hat{i}}{\sqrt{14}}-\frac{3 \hat{j}}{\sqrt{14}}+\frac{\hat{k}}{\sqrt{14}}$
  • B
    $\frac{2 \hat{i}}{\sqrt{14}}-\frac{3 \hat{j}}{\sqrt{14}}-\frac{\hat{k}}{\sqrt{14}}$
  • C
    $\frac{2 \hat{i}}{\sqrt{14}}+\frac{3 \hat{j}}{\sqrt{14}}-\frac{\hat{k}}{\sqrt{14}}$
  • ✓
    $\frac{-2 \hat{i}}{\sqrt{14}}+\frac{3 \hat{j}}{\sqrt{14}}-\frac{\hat{k}}{\sqrt{14}}$
✓

Answer

Correct option: D.
$\frac{-2 \hat{i}}{\sqrt{14}}+\frac{3 \hat{j}}{\sqrt{14}}-\frac{\hat{k}}{\sqrt{14}}$
(D)
$\begin{aligned}
\text { Unit vector }
  =\frac{\text { Vector }}{\text { Modulus of vector }} \\
=\frac{-2 \hat{i}+3 \hat{j}-\hat{k}}{\sqrt{(-2)^2+(3)^2+(-1)^2}} \\
=\frac{-2 \hat{i}+3 \hat{j}-\hat{k}}{\sqrt{(14)}}=\frac{-2 \hat{i}}{\sqrt{14}}+\frac{3 \hat{j}}{\sqrt{14}}-\frac{\hat{k}}{\sqrt{14}}
\end{aligned}$
Hence the correct option is (D).

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