MCQ
The component of vector $\vec A = 2\hat i + 3\hat j$ along the vector $\hat i + \hat j$ is
- ✓$\frac{5}{{\sqrt 2 }}$
- B$10\sqrt 2 $
- C$5\sqrt 2 $
- D$5$
✓
Answer
Correct option: A.
$\frac{5}{{\sqrt 2 }}$
a
Let $\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$
Let $\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$
Component of $\vec{\mathrm{A}}$ in direction of $\overrightarrow{\mathrm{B}}=\frac{(\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}) \overrightarrow{\mathrm{B}}}{\mathrm{B}^{2}}$
$=\frac{(2 \times 1+3 \times 1)(\hat{i}+\hat{j})}{2}=\frac{5}{2}(\hat{i}+\hat{j})$
Magnitude of component $=\frac{5}{\sqrt{2}}$
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