If there are 2 vectors that have equal magnitude, and have the angle (theta) between the two of them, what is the value of (theta) if the resulting vector has the same magnitude as well?

Answer 1

Theta= 120 degrees you can demonstrate this with the law of cosines.

Answer 2

the bisector of the angle between the vectors (the resultant)
... must have a component of half the magnitude from each vector

draw a picture

cos(Θ / 2) = 1/2