# 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

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

#### 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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