Alg. Review: Orthonormal Basis
Question and Solution Attached Below

I'm not sure if I understand the question right. I already determined $\sf ||x||^2 $ and $\sf x • y $. The only part that confuses me is "verify your results by finding x times y explicitly and computing $\sf ||x||^2 $ and $\sf x • y $ directly" how to do that ? or what does it even want me to do?

Question

Alg. Review: Orthonormal Basis 
Question and Solution Attached Below

I'm not sure if I understand the question right. I already determined $\sf ||x||^2 $ and $\sf x •  y $. The only part that confuses me is "verify your results by finding x times y explicitly and computing $\sf ||x||^2 $ and $\sf x •  y $ directly" how to do that ? or what does it even want me to do?

anonymous · Answer

attachment

astrophysics · Answer

Magnitude is $$||x|| = \sqrt{x^2+y^2+z^2}$$ for example

anonymous · Answer

oh wait, give me a sec. I'll try that

anonymous · Answer

yeah that's right, I also got 6 for  $\sf ||x||^2 $  which is the same for the one I got using the theorem.. thanks!

astrophysics · Answer

Yw