What is the scalar product?

• The scalar product (also known as the dot product) is one form in which two vectors can be combined together
• The result of taking the scalar product of two vectors is a?real number
  • i.e. a scalar
• The scalar product of two vectors gives information about the angle between the two vectors
  • If the scalar product is?positive?then the angle between the two vectors is?acute?(less than 90°)
  • If the scalar product is?negative?then the angle between the two vectors is?obtuse?(between 90° and 180°)
  • If the scalar product is?zero?then the angle between the two vectors is?90°?(the two vectors are?perpendicular)

How is the scalar product calculated?

• There are?two methods?for calculating the scalar product
• The most common method used to find the scalar product between the two vectors?v?and?w?is?to find the?sum of the product of each component?in the two vectors

What properties of the scalar product do I need to know?

How do I find the angle between two vectors?

• If two vectors with different directions are placed at the same starting position, they will form an angle between them
• The two formulae for the scalar product can be used together to find this angle
  • This is given in the formula booklet
• To find the angle between two vectors:
  • Calculate the scalar product between them
  • Calculate the magnitude of each vector
  • Use the formula to find cos?θ
  • Use inverse trig to find?θ

How do I know if two vectors are perpendicular?

• If the?scalar product?of two (non-zero) vectors is?zero?then they are?perpendicular
• Two vectors are?perpendicular?if their?scalar product?is?zero
  • The value of cos θ= 0 therefore |v||w|cos θ= 0