two vectors of equal magnitude are added to give resultant which is same magnitude as the two vectors. find the angle between two vector
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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∘
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∘
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two vectors p and q has a sum of 18 and resultant is 12. the resultant is perpendicular to smaller of two vectors. find the value of p and q and angle between them
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hello,sum of 18 means the magnitude of both the vectors.right?
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Answered by
1
ANSWER : 120°
EXPLANATION : 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∘
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