# Is it valid to subtract a position vector of direction E with one of direction W?

## Main Question or Discussion Point

Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?

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Doc Al
Mentor
Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?
They must be treated as vectors. 10 units E minus 10 units W does not equal zero, if that's what you're thinking. (You can only subtract components that are along the same direction.)

mathman
If they are in opposite directions, you can subtract. If E and W mean East and West, you can subtract.

Doc Al
Mentor
If they are in opposite directions, you can subtract. If E and W mean East and West, you can subtract.
Good point! For some reason, I was thinking of East and South, but I'm sure you're right that it means East and West. Good catch. (Oops!)

Doc Al
Mentor
Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?
Let me answer it again, given mathman's clarification:

Yes, you can subtract them since they are parallel. But realize that 10 units W is the same as -10 units E. So 10 E - 10 W = 10 E - (-10 E) = 20 units E.

Make sense?

Is it valid to subtract a position vector of direction E with one of direction W or do they both have to have the same dierction when using the net displacement formula?
In your mind, what is the physical interpretation of the addition/subtraction of such position vectors?

jbriggs444