Q72 / 160 · TS EAMCET 2024 (10 May Shift 1) · Mathematics
If $\vec{a}=4 \hat{i}+5 \hat{j}-3 \hat{k}$ and $\vec{b}=6 \hat{i}-2 \hat{j}-2 \hat{k}$ are two vectors, then the magnitude of the components of parallel to $\vec{a}$ is
- Correct answerA$2 \sqrt{2}$
- B$10 \sqrt{2}$
- C$4 \sqrt{2}$
- D$6 \sqrt{2}$
Solution
$\vec{a}=4 \hat{i}+5 \hat{j}-3 \hat{k}, \vec{b}=6 \hat{i}-2 \hat{j}-2 \hat{k}$
Magnitude of component of $\vec{b}$ parallel to $\vec{a}=\frac{|\vec{b} \cdot \vec{a}|}{|a|}$ $=\frac{|(4 \hat{i}+5 \hat{j}-3 \hat{k}) \cdot(6 \hat{i}-2 \hat{j}-2 \hat{k})|}{\sqrt{50}}=\frac{20}{\sqrt{50}}=2 \sqrt{2}.$
Magnitude of component of $\vec{b}$ parallel to $\vec{a}=\frac{|\vec{b} \cdot \vec{a}|}{|a|}$ $=\frac{|(4 \hat{i}+5 \hat{j}-3 \hat{k}) \cdot(6 \hat{i}-2 \hat{j}-2 \hat{k})|}{\sqrt{50}}=\frac{20}{\sqrt{50}}=2 \sqrt{2}.$
Hence, the correct answer is option: 'A'.