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Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
MCQ
A unit vector along the vector $4 \hat{i}-3 \hat{k}$ is
  • A
    $\frac{1}{7}(4 \hat{i}-3 \hat{k})$
  • ✓
    $\frac{1}{5}(4 \hat{i}-3 \hat{k})$
  • C
    $\frac{1}{\sqrt{7}}(4 \hat{i}-3 \hat{k})$
  • D
    $\frac{1}{\sqrt{5}}(4 \hat{i}-3 \hat{k})$
✓

Answer

Correct option: B.
$\frac{1}{5}(4 \hat{i}-3 \hat{k})$
Let $\vec{v}=4 \hat{i}-3 \hat{k}$
$\therefore|\vec{v}|=\sqrt{4^2+(3)^2}$
$=\sqrt{16+9}=\sqrt{25}=5$
Now, $\hat{v}=$ unit vector along $\vec{v}$
$=\frac{\vec{v}}{|\vec{v}|}=\frac{1}{5}(4 \hat{i}-3 \hat{k})$

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