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?
Theta= 120 degrees you can demonstrate this with the law of cosines.
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
To find the value of the angle (θ) between two vectors that have equal magnitudes and produce a resulting vector with the same magnitude, we can use vector addition.
Let's assume vector A and vector B have the same magnitude, and the angle between them is (θ). When added together, they form a resulting vector, let's call it vector R. Since vector R has the same magnitude, it means that vector A, vector B, and vector R form an equilateral triangle.
Now, in an equilateral triangle, all angles are equal to 60 degrees. Therefore, the angle (θ) between vector A and vector B would also be 60 degrees.
To recap:
If two vectors have equal magnitudes and their resulting vector has the same magnitude, the angle between them is 60 degrees.