SOLUTION: if 'a' and 'b' both are unit vectors then how it is possible that 'a+b' is also a unit vector

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Question 679034: if 'a' and 'b' both are unit vectors then how it is possible that 'a+b' is also a unit vector
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
The conditions needed are:
1)
a%5B1%5D%5E2%2Ba%5B2%5D%5E2=1
2)
b%5B1%5D%5E2%2Bb%5B2%5D%5E2=1


3)
%28a%5B1%5D%2Bb%5B1%5D%29%5E2%2B%28a%5B2%5D%2Bb%5B2%5D%29%5E2=1

This nonlinear system does have solutions, for example
a=1i
b=-1%2F2+%2Ai+%2B+sqrt%283%29%2F2+%2Aj++
is such a pair