Find ` vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i+ hat j+ hat kdot`

Explanation

To find the cross product \( \vec{a} \times \vec{b} \) where \( \vec{a} = 2\hat{i} + \hat{k} \) and \( \vec{b} = \hat{i} + \hat{j} + \hat{k} \), we will use the determinant method. Here are the steps:

### Step-by-Step Solution:

1. **Write the vectors in component form**:
\[ \vec{a} = 2\hat{i} + 0\hat{j} + 1\hat{k} \quad \text{(which can be written as (2, 0, 1))} \]
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