The answers are: u.v = 1/2, and u.w = -1/2.
Why is u.w a minus 1/2?© BrainMass Inc. brainmass.com October 10, 2019, 3:56 am ad1c9bdddf
From the diagram we see that:
u + w = v
w = v - u
u.w = u.(v-u)
Because the dot product is distributive:
u.w = u . (v-u) = u.v - u.u
We know ...
The solution finds u dot v and u dot w (u.v and u.w) from the diagram provided.