Final answer:
The statement about the exterior angle theorem is true. However, knowing only the angles of vectors doesn't allow us to determine the resultant vector's angle. The Pythagorean theorem can be used for vectors at right angles, and knowing one vector's magnitude and both vectors' angles allows us to find the resultant vector's magnitude and direction.
Step-by-step explanation:
The statement, "The exterior angle theorem states that the measure of the exterior angle is equal to the sum of the two remote interior angles," is true. An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles, according to this theorem in geometry.
Regarding vector addition:It is false that if only the angles of two vectors are known, we can determine the angle of their resultant addition vector. The magnitudes of the vectors are also required.The use of the Pythagorean theorem to calculate the length of the resultant vector when two vectors are at right angles to each other is true. The theorem allows us to find the magnitude of the resultant vector, which is the hypotenuse of the right triangle formed by the two vectors.If we know the angles and the magnitude of one vector, it is true that we can find the magnitude and direction of the resultant vector. The other vector's magnitude is necessary to find the exact resultant, and trigonometric methods or the parallelogram law can be applied.