Given vectors \(\vec{A} = 3\hat{i} + 2\hat{j} - 4\hat{k}\) and \(\vec{B} = -2\hat{i} + 3\hat{j} + 5\hat{k}\), find the vector \(\vec{A} - \vec{B}\).

Step 1 ：The subtraction of two vectors is done component-wise. Thus, the difference \(\vec{A} - \vec{B}\) can be calculated as follows:

Step 2 ：\(\vec{A} - \vec{B} = (3\hat{i} + 2\hat{j} - 4\hat{k}) - (-2\hat{i} + 3\hat{j} + 5\hat{k})\)

Step 3 ：= (3 - (-2))\hat{i} + (2 - 3)\hat{j} + (-4 - 5)\hat{k}

Step 4 ：= 5\hat{i} - \hat{j} - 9\hat{k}