If \( \vec{A} = 2\hat{i} - 3\hat{j} - 4\hat{k} \) and \( \vec{B} = \hat{i} + \hat{j} - 5\hat{k} \) then the projection of \( \vec{B} \) on \( \vec{A} \) is:
A \( \frac{19}{\sqrt{27}} \)
B \( \frac{19}{\sqrt{29}} \)
C \( -\frac{19}{27} \)
D \( -\frac{19}{29} \)
Solution
Correct Answer: Option C