As there are 3 sides to the triangle, some information about the third side is also needed to solve the problem. Otherwise some condition or resultant value is needed just as we need two equations to solve them when it contains two variables x and y

For simplicity, let us assume that the resultant is equal to the greatest side.

Let the vectors be A and B such that vector A = B

The resultant vector C is equal to (2)^1/2A

Now as A and B are equal in magnitude and -C is their resultant vector which is root 2 times their magnitude means 
A and B represent adjacent sides of square and -C represent their diagonal.
Therefore angle between A and B is 90 degree

As A = B, angle PQR = angle QRP = 45⁰