Net Displacement: Subtracting E from W Direction Vectors

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Discussion Overview

The discussion revolves around the validity of subtracting position vectors in different directions, specifically East (E) and West (W), within the context of calculating net displacement. Participants explore the implications of vector subtraction and the physical interpretation of these operations.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants assert that position vectors must be treated as vectors and that subtracting vectors in different directions requires careful consideration of their orientations.
  • One participant states that if E and W represent opposite directions, subtraction is valid, suggesting that 10 units E minus 10 units W does not equal zero.
  • Another participant clarifies that 10 units W can be interpreted as -10 units E, leading to a net displacement of 20 units E when calculated correctly.
  • A participant questions the physical interpretation of adding or subtracting position vectors, prompting further exploration of the concept.
  • One participant provides a practical example of driving 10 miles east and then 10 miles west, concluding that the total distance traveled is 20 miles east, which illustrates the concept of net displacement.

Areas of Agreement / Disagreement

Participants express differing views on the conditions under which position vectors can be subtracted. While some agree on the validity of subtraction when vectors are in opposite directions, others emphasize the need for clarity regarding their orientations. The discussion remains unresolved regarding the broader implications of these operations.

Contextual Notes

Participants reference the need for clarity in definitions and interpretations of directional vectors, indicating potential limitations in understanding the net displacement formula. There are also unresolved questions about the physical meaning of vector operations.

ybhathena
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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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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.
 

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