Question

Given that $\vec{A} + \vec{B} = x_1\hat{i} + y_1\hat{j}$ and $\vec{A} - \vec{B} = x_2\hat{i} + y_2\hat{j}$, what is $\vec{B}$? $\vec{B} = \frac{1}{2}(x_1 - x_2)\hat{i} + \frac{1}{2}(y_1 - y_2)\hat{j}$ $\vec{B} = \frac{1}{2}(x_1 + x_2)\hat{i} + \frac{1}{2}(y_1 - y_2)\hat{j}$ $\vec{B} = \frac{1}{2}(x_1 - x_2)\hat{i} + \frac{1}{2}(y_1 + y_2)\hat{j}$ $\vec{B} = \frac{1}{2}(x_1 + x_2)\hat{i} + \frac{1}{2}(y_1 + y_2)\hat{j}$

          Given that \(\vec{A} + \vec{B} = x_1\hat{i} + y_1\hat{j}\) and \(\vec{A} - \vec{B} = x_2\hat{i} + y_2\hat{j}\), what is \(\vec{B}\)?

$\vec{B} = \frac{1}{2}(x_1 - x_2)\hat{i} + \frac{1}{2}(y_1 - y_2)\hat{j}$

$\vec{B} = \frac{1}{2}(x_1 + x_2)\hat{i} + \frac{1}{2}(y_1 - y_2)\hat{j}$

$\vec{B} = \frac{1}{2}(x_1 - x_2)\hat{i} + \frac{1}{2}(y_1 + y_2)\hat{j}$

$\vec{B} = \frac{1}{2}(x_1 + x_2)\hat{i} + \frac{1}{2}(y_1 + y_2)\hat{j}$