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

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?

Doc Al

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

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

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.)

Boston_Guy

In your mind, what is the physical interpretation of the addition/subtraction of such position vectors?

jbriggs444

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.