Question:
The projection vector of \(\vec{a}=\hat{i}-3 \hat{j}-3 \hat{k}\) on \(\vec{b}=3 \hat{i}-4 \hat{j}\) is
The projection vector of \(\vec{a}=\hat{i}-3 \hat{j}-3 \hat{k}\) on \(\vec{b}=3 \hat{i}-4 \hat{j}\) is
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The vector projection of \(\vec a\) on \(\vec b\) is \(\frac{\vec a\cdot\vec b}{|\vec b|^2}\,\vec b\).
Updated On: Nov 12, 2026
- \(\frac{9}{5} \hat{i}-\frac{12}{5} \hat{j}\)
- \(\frac{3}{\sqrt{19}} \hat{i}-\frac{4}{\sqrt{19}} \hat{j}\)
- \(\frac{12}{5} \hat{i}-\frac{36}{5} \hat{j}-\frac{36}{5} \hat{k}\)
- \(9 \hat{i}-12 \hat{j}\)
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The Correct Option is A
Solution and Explanation
\(\vec a\cdot\vec b=(1)(3)+(-3)(-4)+(-3)(0)=3+12=15\) and \(|\vec b|^2=9+16=25\).
Projection vector \(=\frac{15}{25}(3\hat i-4\hat j)=\frac{3}{5}(3\hat i-4\hat j)=\frac{9}{5}\hat i-\frac{12}{5}\hat j\).
Answer: (1) \(\frac{9}{5} \hat{i}-\frac{12}{5} \hat{j}\)
Projection vector \(=\frac{15}{25}(3\hat i-4\hat j)=\frac{3}{5}(3\hat i-4\hat j)=\frac{9}{5}\hat i-\frac{12}{5}\hat j\).
Answer: (1) \(\frac{9}{5} \hat{i}-\frac{12}{5} \hat{j}\)
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