Math 220 Written Assignment 11 Circle your section: Name: Math 220-01 (10:35-11:25) ID#: Math 220-02 (1:25-2:15) Math 220-03 (9:10-10:00) I prefer that you submit your answers on a printed copy of this document, like it's a quiz or exam. However, you may instead rewrite the questions by hand before solving them. Staple sheets together, in order. Be neat. Always give enough work and clear explanation so that fellow students could follow what you did (from start to finish) just by reading your paper. 6 3 1 1. Let u = 2 , v = 1 , w = 3 . 3 5 4 a) Find a unit vector in the direction of v. b) Find the distance between v and w. c) Compute u q v, v q w and u q w. State which pair of vectors is orthogonal. 2. Prove that if x is orthogonal to each of v1 , v2 , . . . , vp , then x is orthogonal to any vector in Span{v1 , v2 , . . . , vp }. 3. Prove that if W is any subspace of Rn , then W is also a subspace of Rn