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'''Calculate the [[Resultant Force]].'''
There is 4[[N]] up and the 7[[N]] down.
F<sub>R</sub> = (+4N) + (-7N)
'''Calculate the [[Resultant Force]].'''
There is 4[[N]] left and the 3[[N]] right.
F<sub>R</sub> = (+3N) + (-4N)
'''Calculate the [[Resultant Force]].'''
There is 6[[N]] up and the 6[[N]] down.
F<sub>Vertical</sub> = (+6N) + (-6N)
F<sub>Vertical</sub> = 0N up
There is 6[[N]] left and the 4[[N]] right.
F<sub>Horizontal</sub> = (+4N) + (-6N)
: When [[force]]s act along the same line but in opposite directions; one is [[Subtraction|subtracted]] from the other.
: When [[force]]s are at [[Right Angle|right angles]] to one another they can be added using [[Pythagoras Theorem|Pythagoras theorem]] to find the [[magnitude]] of the '''resultant force''' and then [[trigonometry]] can be used to find the direction of the '''resultant force'''.
===Examples===
{| class="wikitable"
|[[File:ResultantForce1.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Up is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
There is 29N up and 37N down.
F<sub>R</sub> = (+29N) + (-37N)
F<sub>R</sub> = -8N upwards
|}
{| class="wikitable"
|-
|[[File:ResultantForce2.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Right is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
There is 114N right and 105N left.
F<sub>R</sub> = (+114N) + (-105N)
F<sub>R</sub> = 9N right
|}
{| class="wikitable"
|-
|[[File:ResultantForce3.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Right is [[Positive (Number)|positive]].
Up is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
There is 38N up and 38N down.
F<sub>R</sub> = (+38N) + (-38N)
F<sub>R</sub> = 0N upwards
'''Calculate the [[Resultant Force]]'''
There is 50N right and 40N left.
F<sub>R</sub> = (+50N) + (-40N)
F<sub>R</sub> = 10N right
|}
{| class="wikitable"
|-
|[[File:ResultantForce4.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Right is [[Positive (Number)|positive]].
Up is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
There is 22N up and 16N down.
F<sub>Vertical</sub> = (+22N) + (-16N)
F<sub>Vertical</sub> = 6N upwards
'''Calculate the [[Resultant Force]]'''
There is 26N right and 18N left.
F<sub>Horizontal</sub> = (+26N) + (-18N)
F<sub>Horizontal</sub> = 8N right
|}