Question 1.CA.7: Graphically adding and subtracting vectors Two vectors A and...
Graphically adding and subtracting vectors
Two vectors \overset{\rightarrow }{\pmb{A}} and \overset{\rightarrow }{\pmb{B}} are shown in Figure 1.17. The y component of \overset{\rightarrow }{\pmb{A}} – \overset{\rightarrow }{\pmb{B}} is
A. positive.
B. negative.
Notice that the two vectors are drawn tip to tail, which means that the vector pointing from the origin to the end of vector \overset{\rightarrow }{\pmb{B}} is the vector sum \overset{\rightarrow }{\pmb{A}} + \overset{\rightarrow }{\pmb{B}} . To show \overset{\rightarrow }{\pmb{A}} – \overset{\rightarrow }{\pmb{B}} we need to turn vector \overset{\rightarrow }{\pmb{B}} around so that it points upward and to the left rather than downward and to the right. Since the y component of vector \overset{\rightarrow}{\pmb{A}} points upward and the y component of vector \overset{\rightarrow }{-\pmb{B}} also points upward, \overset{\rightarrow }{\pmb{A}} – \overset{\rightarrow }{\pmb{B}} must point upward. For this choice of coordinate system, where the positive direction for y points upward, answer A is correct.