Find the sine of the angle between the vectors `veca=3hati+hatj+2hatkandvecb=2hati-2hatj+4hatk`

Explanation

To find the sine of the angle between the vectors \(\vec{a} = 3\hat{i} + \hat{j} + 2\hat{k}\) and \(\vec{b} = 2\hat{i} - 2\hat{j} + 4\hat{k}\), we will follow these steps:

### Step 1: Calculate the dot product of the vectors \(\vec{a}\) and \(\vec{b}\).

The dot product \(\vec{a} \cdot \vec{b}\) is calculated as follows:

\[
\vec{a} \cdot \vec{b} = (3\hat{i} + \hat{j} + 2\hat{k}) \cdot (2\hat{i} - 2\hat{j} + 4\hat{k})
...