AP EAMCET · Maths · Vector Algebra
If \(\vec{f}=\hat{i}+\hat{j}+\hat{k}\) and \(\vec{g}=2 \hat{i}-\hat{j}+3 \hat{k}\) then the projection vector of \(\vec{f}\) on \(\vec{g}\) is
- A \(\frac{2}{7}(\hat{i}+\hat{j}+\hat{k})\)
- B \(\frac{2}{7}(2 \hat{i}-\hat{j}+3 \hat{k})\)
- C \(\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\)
- D \(\frac{1}{14}(2 \hat{i}-\hat{j}+3 \hat{k})\)
Answer & Solution
Correct Answer
(B) \(\frac{2}{7}(2 \hat{i}-\hat{j}+3 \hat{k})\)
Step-by-step Solution
Detailed explanation
\(\vec{f}=\hat{i}+\hat{j}+\hat{k} \text { and } \vec{g}=2 \hat{i}-\hat{j}+3 \hat{k}\) Projection of \(\vec{f}\) on \(\vec{g}=\frac{\vec{f} \cdot \vec{g}}{|\vec{g}|^2} \vec{g}\) \(=\frac{(2-1+3)}{(4+1+9)}(2 \hat{i}-\hat{j}+3 \hat{k})=\frac{2}{7}(2 \hat{i}-\hat{j}+3 \hat{k})\)
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