IB DP Maths: AA HL复习笔记3.9.3 Magnitude of a Vector
Magnitude of a Vector
How do you find the magnitude of a vector?
- The?magnitude?of a vector tells us its?size?or?length
- For a?displacement?vector it tells us the?distance?between the two points
- For a?position?vector it tells us the?distance?of the point from the?origin
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This is given in the formula booklet
How do I find the distance between two points?
- Vectors?can be used to find the distance (or displacement) between two points
- It is the?magnitude?of the vector between them
- Given the?position vectors?of two points:
- Find the displacement vector between them
- Find the magnitude of the displacement vector between them
Exam Tip
- Finding the magnitude of a vector is the same as finding the distance between two coordinates, it is a useful formula to commit to memory in order to save time in the exam, however it is in your formula booklet if you need it
Worked Example
Find the magnitude of the vector AB = 4i?–?j?+ 2k.
Unit Vectors
What is a unit vector?
- A?unit vector?has a?magnitude?of 1
- It can be found by dividing a vector by its?magnitude
- This will result in a vector with a size of 1 unit in the direction of the original vector
Exam Tip
- Finding the unit vector will not be a question on its own but will be a useful skill for further vectors problems so it is important to be confident with it
Worked Example
Find the unit vector in the direction 2i?– 2j?+?k.
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