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The resultant of vec(A)+vec(B) is vec(R ...

The resultant of `vec(A)+vec(B) is vec(R )_(1)`. On reversing the vector `vec(B)`, the resultant becomes `vec(R )_(2)`. What is the value of `R_(1)^(2)+R_(2)^(2)`?

A

`A^2+B^2`

B

`A^2-B^2`

C

`2(A^2+B^2)`

D

`2(A^2-B^2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec( R)_1=vec(A)+vec(B),vecR_2=vecA-vecB`
`R_1^(2)+R_2^(2)=(sqrt(A^(2)+B^(2)))^(2)+(sqrt(A^(2)+B^(2)))^(2)=2(A^(2)+B^(2))`
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