- #1

keroberous

- 15

- 1

"If the magnitude of a+b equals the magnitude of a+c then this implies that the magnitudes of b and c are equal. Is this true or false?"

The textbook says that this statement is true, but I'm inclined to believe it is false. I made a quick sketch to show my thinking visually.

I drew these diagrams to scale, so vector a is the same in each case and the lengths of a+b and a+c are in fact equal (both 5 cm). It's clear to me that b and c are different lengths/magnitudes here. I'm not sure if the text made an error (not unheard of) or if I made an incorrect assumption somewhere. Thanks!