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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