CIE A Level Maths: Pure 3复习笔记7.1.2 Magnitude & Direction

Magnitude & Direction

What is the magnitude of a vector?

  • The magnitude of a vector is simply its size
  • It also tells us the distance between two points
  • You can find the magnitude of a vector using Pythagoras’ theorem

11.1.2-Magnitude-Direction-Diagram-1a

  • To work out the unit vector in the direction of a given vector
  • unit vector has a magnitude of 1So to find the unit vector of a given vector, divide by its magnitude

11.1.2-Magnitude-Direction-Diagram-1b

What is the direction of a vector?

  • Vectors have opposite direction if they are the same size but opposite signs

  • The direction of a vector is what makes it more than just a scalar
    • Eg. two objects with velocities of 7 m/s and ‑7 m/s are travelling at the same speed but in opposite directions
  • Two vectors are parallel if and only if one is a scalar multiple of the other
  • For real-life contexts such as mechanics, direction can be calculated from a given vector using trigonometry (see Right-Angled Triangles)
  • It is usually calculated anticlockwise from the positive x-axis (unless otherwise stated eg. a bearing)

How do I write a vector in component form?

  • We have already seen that vectors can be written in different forms
  • Component form means writing a vector in terms of i and j components
  • Given the magnitude and direction of a vector you can work out its components and vice versa

11.1.2-Magnitude-Direction-Diagram-3a11.1.2-Magnitude-Direction-Diagram-3b

Exam Tip

  • Diagrams can help, especially when working out direction – if there isn’t a diagram, draw one.
  • Remember, resolving a vector just means writing it in component form.

Worked Example

11.1.2-Magnitude-Direction-Example-Solution

 

 

 

 

 

 

转载自saveemyexams

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