Answer to Question #145416 in Physics for Kelly

Question

If the vectors x and y are mutually perpendicular and |x| = 7, |y| = 24, draw in one diagram:

I) x + y (ii) x - y

b) calculate |x + y| and |x - y|

Answer 1

a) Diagram

b) As one can see from the diagram, $|\mathbf{x} + \mathbf{y}| = |\mathbf{x}-\mathbf{y}|$. Thus, using the Pythagorean theorem, find:

$$|\mathbf{x} + \mathbf{y}| = \sqrt{|\mathbf{x}|^2 + |\mathbf{y}|^2} = \sqrt{7^2 + 24^2} =25$$

Answer. $|\mathbf{x} + \mathbf{y}| =|\mathbf{x} - \mathbf{y}| = 25$