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
• The magnitude of a vector ?is written?when typed (or ?when handwritten)

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

What is the direction of a vector?

• Vectors have opposite direction if they are the same size but opposite signs
  • e.g. if or ? then - or
• 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