Essential University Physics: Volume 1 (4th Edition)

$\vec{A}\cdot \vec{B}=A_xB_x + A_yB_y+A_zC_z$
a) Anything dotted with itself is one, so the value of all of these dot products (also known as scalar products) is one. b) We know that anything dotted with a different unit vector is 0, so the value of all of these dot products is 0. c) Using the distributive property and the results from a) and b), we find: $\vec{A}\cdot \vec{B}=A_xB_x + A_yB_y+A_zC_z$