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Vector Methods:
Equilibrant vs Resultant:
The equilibrant is the opposite of the resultant, it has the same length/
magnitude, but the direction is opposite.
• A + B + C = R
• -(A + B + C)= E
• E=-R
• A basic sketch is the most straight forward way to check the magnitude and direction.
Cartesian, Rectangular and
Polar format:
• Sum the i and j values
• Convert the i, j totals back into Polar to get the magnitude r and the direction q
• Use the Rec and Pol functions on a scientific calculator
Otherwise use:- 𝑖 = 𝑟𝑐𝑜𝑠𝜃 𝑎𝑛𝑑 𝑗 = 𝑟𝑠𝑖𝑛𝜃
𝑟 = 𝑖2 + 𝑗2 and 𝜃 = 𝑡𝑎𝑛−1 𝑗
𝑖
q Values start on the horizontal and increase anticlockwise

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  • 2. Equilibrant vs Resultant: The equilibrant is the opposite of the resultant, it has the same length/ magnitude, but the direction is opposite. • A + B + C = R • -(A + B + C)= E • E=-R • A basic sketch is the most straight forward way to check the magnitude and direction.
  • 3. Cartesian, Rectangular and Polar format: • Sum the i and j values • Convert the i, j totals back into Polar to get the magnitude r and the direction q • Use the Rec and Pol functions on a scientific calculator Otherwise use:- 𝑖 = 𝑟𝑐𝑜𝑠𝜃 𝑎𝑛𝑑 𝑗 = 𝑟𝑠𝑖𝑛𝜃 𝑟 = 𝑖2 + 𝑗2 and 𝜃 = 𝑡𝑎𝑛−1 𝑗 𝑖 q Values start on the horizontal and increase anticlockwise