Vectors Problem - Sketch a diagram(s) that supports the fact that -(u + v) = - u-v

Question

There are little arrows on top of u and v pointing right (the format won't let me add it)

Answer 1

Hi Amanda M.,

It's really quite simple. Start at the origin, draw general vector u, then general vector v from the tip of u. The combined figure defines a net displacement of (u + v) (from the origin to the tip of v). Now, the negative displacement of that goes the opposite way from the origin. And if you draw the reflection of each of the vectors u and v (as they are on your sketch already), across the origin, you will see that the defined resulting figure (the symmetrical reflection of your initial sketch of (u+v)) defines the condition you are asked to show.

Isn't reflection wonderful?

-- Cheers, --Mr. d.