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Chapter 1.CA

Q. 1.CA.7

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.

1.17

Step-by-Step

Verified Solution

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.