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Position Vectors (CIE A Level Maths: Pure 3)
Revision Note
Position Vectors
What is a position vector?
- Position vectors describe the position of a point in relation to the origin
- They are different to displacement vectors which describe the direction and distance between any two points
Distance between two points
- The distance between two points is the magnitude of the vector between them (see Magnitude Direction)
How do I find the magnitude of a displacement vector?
- You can use coordinate geometry to find magnitudes of displacement vectors from A to B
- From the position vectors of A and B you know their coordinates
- If , then point A has coordinates
- If , then point B has coordinates
- The distance between two points is given by
- So
- For example, if points A and B have position vectors and respectively
- then
- From the position vectors of A and B you know their coordinates
- Alternatively, you could find by
- first using to find in vector form
- and then calculating its magnitude directly
- See the Worked Example below
- first using to find in vector form
Examiner Tip
- Remember if asked for a position vector, you must find the vector all the way from the origin.
- Diagrams can help, if there isn’t one, draw one.
Worked example
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