If `vec(A)=2hat(i)+3hat(j)-hat(k)` and `vec(B)=-hat(i)+3hat(j)+4hat(k)`, then find the projection of `vec(A)` on `vec(B)`.

Explanation

To find the projection of vector \(\vec{A}\) on vector \(\vec{B}\), we can use the formula for the projection of one vector onto another. The projection of vector \(\vec{A}\) onto vector \(\vec{B}\) is given by:

\[ \text{proj}_{\vec{B}} \vec{A} = \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|^2} \vec{B} \]

Where:
- \(\vec{A} \cdot \vec{B}\) is the dot product of vectors \(\vec{A}\) and \(\vec{B}\).
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