Find the angle between force `vecF=(5hati+5hatj+5hatk)` unit and displacement `vecd=(3hati+4hatj-3hatk)` unit Also find the projection of `vecF on vecd.`

Explanation

To solve the problem of finding the angle between the force vector \(\vec{F} = (5\hat{i} + 5\hat{j} + 5\hat{k})\) and the displacement vector \(\vec{d} = (3\hat{i} + 4\hat{j} - 3\hat{k})\), as well as the projection of \(\vec{F}\) on \(\vec{d}\), we will follow these steps:

### Step 1: Calculate the Dot Product of \(\vec{F}\) and \(\vec{d}\)

The dot product \(\vec{F} \cdot \vec{d}\) is calculated as follows:

\[
\vec{F} \cdot \vec{d} = (5)(3) + (5)(4) + (5)(-3)
...