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In a plane, add a 120 N force at 300 and a -100 N force at 900 using the parallelogram method. [111N 339]

User AMolina
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See the attached figure.

The black arrows represent the two given vectors. The dashed black arrows are these same vectors, but translated so that the end of one vector is aligned with the start of another.

The red vector is their sum.

In case you also need to find the magnitude and direction of the sum, we have

A = (120 N) (cos(30°) i + sin(30°) j) = (60√3 i + 60 j) N

B = (-100 N) (cos(90°) i + sin(90°) j) = (-100 j) N

⇒ A + B = (60√3 i - 40 j) N

⇒ ||A + B|| = √((60√3)² + (-40)²) N = 20√31 N

and its direction relative to the positive horizontal axis (rightward) is θ such that

tan(θ) = (-40) / (60√3) = -2/(3√3)

⇒ θ = arctan(-2/(3√3)) ≈ -21.05°

In a plane, add a 120 N force at 300 and a -100 N force at 900 using the parallelogram-example-1
User Andreas Lochbihler
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