If `| vec a|=2,\ | vec b|=7\ a n d\ vec axx vec b=3 hat i+2 hat j+6 hat k ,\ ` find the angle between ` vec a\ a n d\ vec bdot`

Explanation

To find the angle between the vectors \( \vec{a} \) and \( \vec{b} \), we can use the formula for the magnitude of the cross product:

\[ |\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin \theta \]

### Step 1: Calculate the magnitude of the cross product
Given that \( \vec{a} \times \vec{b} = 3\hat{i} + 2\hat{j} + 6\hat{k} \), we first need to find the magnitude of \( \vec{a} \times \vec{b} \):
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