(A) Using unit vector notation, A = 2i − 3j and B = −4i +2j. Adding components,
we see that A + B = (2 + [−4])i + ([−3] + 2)j = −2i − j. Therefore, the x-
component of the sum is −2 and the y-component is −1.
(B) A − B = (2i − 3j) − (−4i + 2j) = (2 − [−4])i + (−3 − 2)j = 6i − 5j. The x-
component is 6 and the y-component is −5.
(C) 2A = 2(2i − 3j) = 4i − 6j. 4 and −6 are the x- and y-components, respectively.
(D) A + 3B = (2i − 3j) + 3(−4i + 2j) = (2 + 3 [−4])i + (−3 + 3 [2])j =
−10i + 3j. −10 and 3 are the x- and y-components, respectively.
Magnitude of a Vector
Magnitude is a scalar number indicating the length of a vector. Use the Pythagorean
theorem! You can use components Cx and Cy to find the magnitude of the new vector
C.