Net Displacement: Subtracting E from W Direction Vectors

AI Thread Summary
Subtracting position vectors in different directions is valid as long as they are treated as vectors. Specifically, when dealing with directions like East (E) and West (W), one can subtract them since they are opposite vectors. For example, 10 units E minus 10 units W results in a total of 20 units E, illustrating that the net displacement accounts for direction. The discussion emphasizes understanding the physical interpretation of these vectors in real-world scenarios, such as driving distances. Overall, the key takeaway is that directionality matters in vector subtraction for accurate net displacement calculations.
ybhathena
Messages
42
Reaction score
0
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?
 
Physics news on Phys.org
ybhathena said:
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.)
 
If they are in opposite directions, you can subtract. If E and W mean East and West, you can subtract.
 
mathman said:
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!)
 
ybhathena said:
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.)
 
ybhathena said:
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 traveled to the east.
 
Back
Top