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

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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 Quote by ybhathena 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.)
 Recognitions: Science Advisor If they are in opposite directions, you can subtract. If E and W mean East and West, you can subtract.

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

 Quote by mathman 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!)

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 Quote by ybhathena 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?

(Glad that mathman was awake.)

 Quote by ybhathena 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?
 If I drive 10 miles east, turn around, put the car in reverse and drive another 10 miles while facing west, the result is 20 miles travelled to the east.
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