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If a and b are two unit vectors such that a+b is also a unit vector, then find the angle between a and b - Mathematics

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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`

Concept: Product of Two Vectors - Scalar (Or Dot) Product of Two Vectors
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