Theory question 108
VectorsForces of magnitude 3N, 4 N and 2 N act along the vectors j, −i + j and i + j respectively. Calculate, correct to one decimal place, the magnitude of the resultant of the forces.
Show the model answer
Model answer
Unit vectors: j, (−i + j)/√2, (i + j)/√2.
Forces: 3j; 4(−i + j)/√2 = −2.828i + 2.828j; 2(i + j)/√2 = 1.414i + 1.414j.
Resultant = −1.414i + 7.243j; magnitude = √(2 + 52.46) ≈ 7.4 N.
Explanation
Scale each direction to a unit vector before multiplying by the force.