Find the sum of two vectors overrightarrow (A) and overrightarrow (B) lying in the xy plane and given by overrightarrow (A)=(2.0hat (i)+2.0hat (j)) and overrightarrow (B)=(2.0hat (i)-4.0hat (j))

To find the sum of two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$, we simply add their corresponding components. Given:<br /><br />$\overrightarrow{A} = 2.0\hat{i} + 2.0\hat{j}$<br /><br />$\overrightarrow{B} = 2.0\hat{i} - 4.0\hat{j}$<br /><br />The sum of $\overrightarrow{A}$ and $\overrightarrow{B}$ is:<br /><br />$\overrightarrow{A} + \overrightarrow{B} = (2.0\hat{i} + 2.0\hat{i}) + (2.0\hat{j} - 4.0\hat{j})$<br /><br />$= 4.0\hat{i} - 2.0\hat{j}$<br /><br />Therefore, the sum of the two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is $\overrightarrow{A} + \overrightarrow{B} = 4.0\hat{i} - 2.0\hat{j}$.