In order to use the pythagorean theorem to find the magnitude of a resultant vector, which must be true regarding the two initial vectors?
a)they form a 90 degree angle.
b)they are equal in magnitude.
c)they have the same directions.
d)they are parallel to one another.

The true option is a) they form a 90 degree angle.

Pythagorean theorem is valid for right triangles, which is what you can form when the two vectors have a 90 degree angle.

Regarding the other options:

b) They are equal in magnitude: this is not a condition because Pythagoream theorem is valid for any magnitude as long as the angle is 90°C.

c) They have the sam directions: false, because if the two vectors have the same directions the magnitud is the sum of the two magnitudes.

d) They are parallel: false for a similar reason that c) taking into account if they have the same direction or are opposed.  .