Question

Suppose that u and v are orthogonal vectors in R^n. Find the value of the expression <3u-v. 3u+v>.

Answer 1

The notation used here "<x,y>" is the way they represent the dot product of vector x and vector y in my current textbook

Answer 2

you can distribute in the dot product so use FOIL and then bear in mind that \(\mathbf u \bullet \mathbf v = 0 \) and vice versa

Answer 3

if that worries you, start with this idea and expand it out to 4 vectors


\[ \mathbf A \cdot ( \mathbf B + \mathbf C ) = \mathbf A \cdot \mathbf B + \mathbf A \cdot \mathbf C .\]

now let \(\mathbf A = \mathbf D + \mathbf E \)