• Vectors?are represented by an arrow
  • The?arrowhead?indicates the?direction?of the vector
  • The?length?of the arrow represents the?magnitude

Combining Vectors

• Vectors can be combined by?adding?or?subtracting?them to produce the?resultant vector
  • The?resultant vector?is sometimes known as the ‘net’ vector (eg. the net force)

• There are two methods that can be used to combine vectors: the?triangle method?and the?parallelogram method

• To combine vectors using the triangle method:
  • Step 1:?link the vectors head-to-tail
  • Step 2:?the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

• To combine vectors using the parallelogram method:
  • Step 1:?link the vectors tail-to-tail
  • Step 2:?complete the resulting parallelogram
  • Step 3:?the resultant vector is the diagonal of the parallelogram

Resolving Vectors

• Two vectors can be represented by a single?resultant vector
  • Resolving a vector is the opposite of adding vectors
• A single resultant vector can be resolved
  • This means it can be represented by?two?vectors, which in combination have the same effect as the original one
• When a single resultant vector is broken down into its?parts, those parts are called?components
• For example, a force vector of magnitude?F?and an angle of?θ?to the horizontal is shown below

The resultant force F at an angle θ to the horizontal

• It is possible to?resolve?this vector into its?horizontal?and?vertical?components using trigonometry

The resultant force F can be split into its horizontal and vertical components

• For the?horizontal?component,?F_x?=?F?cos?θ
• For the?vertical?component,?F_y?=?F?sin?θ

Step 4: State the final answer complete with direction

R?= 2√34 = 11.66 =?12 km

θ?=?59°?east and upwards from the horizontal