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Question
If `veca ` and `vecb` are two unit vectors such that `veca+vecb` is also a unit vector, then find the angle between `veca` and `vecb`
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Solution
Given: `veca` and `vec b` are unit vectors
`therefore |veca|=|vecb|=1`
Let the angle between ` veca and vecb "be " theta`
It is given that, `(veca+vecb)` is a unit vector
`therefore |veca+vecb|=1`
`(veca+vecb)(veca+vecb)=1`
`|veca|^2+2veca.vecb+|vecb|^2=1`
`|veca|^2+2|veca|.|vecb|+|vecb|^2=1`
`1+2xx1xx1xxcostheta+1=1`
`2costheta=-1`
`cos theta=-1/2`
`therefore theta=(2pi)/3`
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