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## Q. 1.CA.7

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. ## 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.