Question

if two vectors of equal magnitude four and angle is equal to 120 degrees then find the magnitude and direction of the sum of the vectors

Answer 1

The angle between vector A and vector B is θ as shown above.

The resultant is shown in red. Using the cosine rule:

R2=A2+B2−2AB(cosβ)

But the magnitude of each vector is the same, therefore

A2=A2+A2−2(A)(A)(cosβ)

cosβ=−A2−2(A2)

β=60∘

θ=180∘−60∘=120∘

Answer 2

The angle between vector A and vector B is θθas shown above.

The resultant is shown in red. Using the cosine rule:

R2=A2+B2−2AB(cosβ)R2=A2+B2−2AB(cosβ)

But the magnitude of each vector is the same, therefore

A2=A2+A2−2(A)(A)(cosβ)A2=A2+A2−2(A)(A)(cosβ)

cosβ=−A2−2(A2)cosβ=−A2−2(A2)

β=60∘β=60∘

θ=180∘−60∘=120∘θ=180∘−60∘=120

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