а) (λa+μb)(νa+τb) = λνa^2 + λτab + μνba + μτb^2= λν(α^2m^2 + 2αβmn + β^2n^2) + λτ(αm + βn)(γm + δn) + μν(αm + βn)(γm + δn) + μτ(γ^2m^2 + 2γδmn + δ^2n^2)= λν(α^2k^2 + 2αβklcosφ + β^2l^2) + λτ(αγk^2 + (αδ + βγ)klcosφ + βδl^2) + μν(αγk^2 + (αδ + βγ)klcosφ + βδl^2) + μτ(γ^2k^2 + 2γδklcosφ + δ^2l^2)= -21(25 - 30 + 16) + (-239 - 20 + 36) + (1/339 - 20 + 36) + ((3)^29 + 2615(1/2) + (6)^225)= -2*(-11) + (-54 - 20 + 36) + (9 - 20 + 36) + (81 + 180 + 150)= 22 + (-38) + 25 + 411= 420
б) пр(νa+τb) = (a,νa+τb) = ν(a,a) + τ(a,b)= ν(α^2m^2 + 2αβmn + β^2n^2) + τ(αm + βn)(γm + δn)= 1(25 - 30 + 16) + 2(9 - 20 + 36)= 11 + (-22 + 72)= 61
в) cos(a,τb) = (a,τb)/(ab)= ((-5α - 4β)(2γ + 6δ))/(αγ + βδ)= ((-5(-5) - 4(-4))(23 + 66))/(-53 + -46)= (25 + 16)(6 + 36)/(-15 - 24)= 4142/(-39)= -1764/39
а) (λa+μb)(νa+τb) = λνa^2 + λτab + μνba + μτb^2
= λν(α^2m^2 + 2αβmn + β^2n^2) + λτ(αm + βn)(γm + δn) + μν(αm + βn)(γm + δn) + μτ(γ^2m^2 + 2γδmn + δ^2n^2)
= λν(α^2k^2 + 2αβklcosφ + β^2l^2) + λτ(αγk^2 + (αδ + βγ)klcosφ + βδl^2) + μν(αγk^2 + (αδ + βγ)klcosφ + βδl^2) + μτ(γ^2k^2 + 2γδklcosφ + δ^2l^2)
= -21(25 - 30 + 16) + (-239 - 20 + 36) + (1/339 - 20 + 36) + ((3)^29 + 2615(1/2) + (6)^225)
= -2*(-11) + (-54 - 20 + 36) + (9 - 20 + 36) + (81 + 180 + 150)
= 22 + (-38) + 25 + 411
= 420
б) пр(νa+τb) = (a,νa+τb) = ν(a,a) + τ(a,b)
= ν(α^2m^2 + 2αβmn + β^2n^2) + τ(αm + βn)(γm + δn)
= 1(25 - 30 + 16) + 2(9 - 20 + 36)
= 11 + (-22 + 72)
= 61
в) cos(a,τb) = (a,τb)/(ab)
= ((-5α - 4β)(2γ + 6δ))/(αγ + βδ)
= ((-5(-5) - 4(-4))(23 + 66))/(-53 + -46)
= (25 + 16)(6 + 36)/(-15 - 24)
= 4142/(-39)
= -1764/39