Question

You may complete this on Colab or a local Jupyter notebook. Please ensure that you are submitting your notebook after everything has run so that the TAs can see your results before re-running it themselves.

a) True
b) False

Answer 1

The statement asking if the Pythagorean theorem can be used to calculate the length of the resultant vector from two perpendicular vectors is true; the theorem applies directly to find the magnitude of the resultant.

Step-by-step explanation:

The statement is true. The Pythagorean theorem can indeed be used to calculate the length of the resultant vector when two vectors are at right angles to each other. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. When dealing with vectors, if we have two orthogonal vectors (meaning they are at 90 degrees to each other), they form the two sides of a right-angled triangle. The resultant vector forms the hypotenuse.

Therefore, if we have vectors A and B which are perpendicular, and R is the resultant vector, we can write:

• A² + B² = R²

We can solve for R using:

• R = √(A² + B²)

This is a direct application of the Pythagorean theorem to find the magnitude of the resultant vector.