Two vectors are given by overrightarrow (A)=2overrightarrow (i)+3overrightarrow (j) and overrightarrow (B)=4overrightarrow (i)-3overrightarrow (j) Find: (a) the magnitude and direction of the vector sum overrightarrow (R)=overrightarrow (A)+overrightarrow (B) (b) the magnitude and direction of the vector difference overrightarrow (S)=overrightarrow (A)-overrightarrow (B)

(a) To find the magnitude and direction of the vector sum , we first calculate the sum of the two vectors: The magnitude of is given by the square root of the sum of the squares of its components: The direction of is along the positive x-axis since it has no y-component.(b) To find the magnitude and direction of the vector difference , we calculate the difference of the two vectors: The magnitude of is given by the square root of the sum of the squares of its components: The direction of is 126.87 degrees counterclockwise from the positive x-axis, which can be calculated using the arctangent function: Since the direction is negative, we add 360 degrees to get the positive angle: Therefore, the magnitude and direction of the vector sum are 6 and along the positive x-axis, respectively. The magnitude and direction of the vector difference are and 126.87 degrees counterclockwise from the positive x-axis, respectively.