Final answer:
A vector can indeed form a right-angle triangle with its x and y components, and the Pythagorean theorem can be applied to calculate the resultant vector when two vectors are at right angles. However, you cannot find the resultant vector's angle with only the knowledge of the angles of two vectors; the magnitudes are also needed. Knowing the angles and magnitude of one vector does allow for the resultant's magnitude and direction to be found.
Step-by-step explanation:
True or False: A vector can form the shape of a right angle triangle with its x and y components. The answer is true. Every vector in a plane can be represented as having horizontal (x-component) and vertical (y-component) parts, which forms a right triangle when these components are drawn starting from a common point.
True or False: We can use Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other. This statement is also true. When two vectors are perpendicular, their magnitudes can be treated as the legs of a right triangle, and the resultant vector's magnitude is the hypotenuse. The Pythagorean theorem is the appropriate tool to use here.
True or False: If only the angles of two vectors are known, we can find the angle of their resultant addition vector. This statement is generally false. Without knowing the magnitudes of the vectors, you cannot accurately determine the angle of the resultant vector.
True or False: We can find the magnitude and direction of the resultant vector if we know the angles of two vectors and the magnitude of one. This statement is true, with the information given, you can calculate the resultant vector using trigonometric relationships.