Projection of $\hat{i}+2 \hat{j}+3 \hat{k}$ on $\hat{i}-2 \hat{j}-2 \hat{k}$ is equal to:
Answer & explanation
Correct answer: option 2
Projection of $\vec{a}$ on $\vec{b}$ is $\frac{\vec{a} . \vec{b}}{|\vec{b}|}$
Thus required projection
$=\frac{(\hat{i}+2 \hat{j}+3 \hat{k}) .(\hat{i}-2 \hat{j}-2 \hat{k})}{\sqrt{1+4+4}}$
$=\frac{1-4-6}{3}=-3$
Hence (2) is correct answer.