Question

In the given setup where ABC is a straight line and squares ABXY and BCPQ are on the same side of AC, prove that Px² + CY² = 3(AB² + BQ²).

A. True
B. False

Answer 1

Yes, we can use the Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors at right angles.

Step-by-step explanation:

We can use the Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors that are at right angles to each other. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the two vectors that are at right angles can be represented as the legs of a right triangle, and the resultant vector is the hypotenuse.

For example, if we have two vectors with lengths of 3 units and 4 units that are at right angles to each other, we can use the Pythagorean theorem to find the length of the resultant vector:

c = √(a² + b²) = √(3² + 4²) = √25 = 5 units