Question

Given the displacement vector →D=(3ˆi−4ˆj)m, find the displacement vector →R so that →D+→R=−4Dˆj.

a) →R = (-3ˆi - 4ˆj)m
b) →R = (-7ˆi + 4ˆj)m
c) →R = (3ˆi + 8ˆj)m
d) →R = (7ˆi - 4ˆj)m

Answer 1

The correct displacement vector →R that when added to →D=(3ˆi−4ˆj)m results in −4ˆj is →R = (-3ˆi - 4ˆj)m, accounting for the x-component, as the y-component cancels out.

Step-by-step explanation:

The question involves finding the displacement vector →R so that when added to the displacement vector →D=(3ˆi−4ˆj)m, the result is −4ˆj. We can set up the equation as:

→D + →R = −4ˆj

Given →D=(3ˆi−4ˆj)m, we need to find →R that makes the equation true. If we substitute →D in the equation above, we have:

(3ˆi−4ˆj) + →R = −4ˆj

To find →R, we solve for →R:

→R = −4ˆj - (3ˆi−4ˆj)

→R must be

→R = −3ˆi + 0ˆj

Which simplifies to:

→R = (-3ˆi)m

Therefore, the correct answer is a) →R = (-3ˆi - 4ˆj)m, which accounts for the x-component only as the y-component cancels out.