Defining a displacement vector not touching the origin

In summary, the conversation discusses the representation of vectors and their position in relation to magnitude and direction. It also addresses the concept of shifting vectors and its applicability to displacement vectors.
  • #1
Hijaz Aslam
66
1
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In the diagram let the magnitude of the vector BC and OA are 'x'. I am confused with this part. Vectorially we don't say that the vector BC is ##-x##, because ##-x## is represented by OA. Then how do we represent BC?

It's said a the position of a vector doesn't matter, I mean one can shift it in any way unless their magnitude and direction are changed, is it applicable to a displacement vector? As in the case above we just can't shift the vector ##-x## to BC and call it ##-x##. For instance in the case of a ball thrown from a tower. If we take the origin as the top of the tower, we can always say the last ##x## meters of the tower. Am I confusing any concept?
 
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  • #2
Yes, you are confusing "vector" with a specific interval, "the last x meters of a tower".
 

1. What is a displacement vector?

A displacement vector is a mathematical representation of a change in position or location. It is defined by both magnitude (length) and direction.

2. How is a displacement vector different from a regular vector?

A displacement vector specifically represents a change in position, while a regular vector can represent any quantity with both magnitude and direction.

3. Can a displacement vector start or end at any point?

No, a displacement vector must start at the initial position and end at the final position. It cannot start or end at any other point along its path.

4. How is a displacement vector represented?

A displacement vector is typically represented by an arrow pointing from the initial position to the final position. The length of the arrow represents the magnitude of the displacement, and the direction of the arrow represents the direction of the displacement.

5. What does it mean for a displacement vector to not touch the origin?

This means that the initial position and final position are not at the same point. In other words, the displacement vector does not start and end at the same location. It can start at any point, but it must end at a different point.

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