Find the values of x, y and z so that the vectors ` vec a=x hat i+2 hat j+z hat k`and ` vec b=2 hat i+y hat j+ hat k`are equal.

Explanation

To solve the problem of finding the values of \( x \), \( y \), and \( z \) such that the vectors \( \vec{a} = x \hat{i} + 2 \hat{j} + z \hat{k} \) and \( \vec{b} = 2 \hat{i} + y \hat{j} + \hat{k} \) are equal, we will follow these steps:

### Step 1: Set the vectors equal to each other
Since the vectors \( \vec{a} \) and \( \vec{b} \) are equal, we can write:
\[ x \hat{i} + 2 \hat{j} + z \hat{k} = 2 \hat{i} + y \hat{j} + \hat{k} \]

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