1. (1 point) Find the norm of and the unit vector in the direction of Xif a X= |||| HEI 7= 2. (1 point) Find the angle a between the vectors

3 3 B-0 and 4 2 2 nin 3. (1 point) Find the length of the vector x = |||| = 4. (1 point) Find the angle a between the vectors 6 [2] and [$]- 5. (1 point) Find the length of the vector x = |||| = 6. (1 point) Find the dot product of I= --[1] - x-y= -=[3]. and y= x-y=. 7. (1 point) Find the dot product of B -5 x= [¹] and y=[²]. X= 8 -6 a 8. (1 point) Let (21, 22, 23, 24, és, és) be the standard basis in R6. Find the length of the vector = 47₁-272 − 3ē3 − 3ēs +3ẻs +376 |||||=. 9. (1 point) Suppose =(4,2,0), = (1,1,1) and = (0,-2,5). Then: 7-V = ū.(V+W) = 10. (1 point) Let (u₁,u₂, u3} be an orthonormal basis for an inner product space V. If v=au₁ +bu₂+cuz is so that ||v|| = 40, v is orthogonal to us, and (v, u₂) = -40, find the possible values for a, b, and e. a=. ,b= 11. (1 point) Find a non-zero vector perpendicular to the vector il= -[=] 12. (1 point) Let V= V= Find a basis of the subspace of R+ consisting of all vectors per- pendicular to v. [EHEME] 13. (1 point) Let -0.5 -0.5 -0.5 0.5 V₁ 0.5 0.5 -0.5 0.5 V3 = -0.5 0.5 0.5 0.5 Find a vector V4 in R+ such that the vectors V₁, V₂, V3, and V4 are orthonormal./nV4 -E] 14. (1 point) Generated by Well Work, http://webwork.maa.org, Mathematical Association of America Find the value of k for which the vectors 8-8 and -4 are orthogonal. 77-7 Ņm in wat 5