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

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