5 la+Bl=(a+B, a+ B) =(a,a)+(a,B)+(B,a)+(B,B) (a,a)+(B,) lal|2+‖/‖2 18.在欧氏空间中,求a,B之间的夹角,其中 (1)a=[1,2,2,3],B=B3,1,5,1]r (2)a=[2,1,3,2y,B=[1,2,-2,1 3)a=[1,3,-5,1,B=②2,-1,2,-3]1 解: <a,B>=c1(a,B) √8×36 T <aB>=cOs la‖‖ E cOS E cOS5 kα + βk 2 = (α + β, α + β) = (α, α) + (α, β) + (β, α) + (β, β) = (α, α) + (β, β) = kαk 2 + kβk 2 18. 3Óºòm•ß¶α, βÉmYߟ• (1) α = [1, 2, 2, 3]T , β = [3, 1, 5, 1]T (2) α = [2, 1, 3, 2]T , β = [1, 2, −2, 1]T (3) α = [−1, 3, −5, 1]T , β = [2, −1, 2, −3]T )µ (1) < α, β > = cos−1 (α, β) kαkkβk = cos−1 18 √ 18 × 36 = cos−1 √ 2 2 = π 4 (2) < α, β > = cos−1 (α, β) kαkkβk = cos−1 0 = π 2 (3) < α, β > = cos−1 (α, β) kαkkβk = cos−1 −18 √ 36 × 18 = cos−1 − √ 2 2 = − π 4