Ryabushko A.P. IDZ 2.1 option 17

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DHS - 2.1
№ 1.17. Given a vector a = α · m + β · n; b = γ · m + δ · n; | M | = k; | N | = ℓ; (M; n) = φ;
Find: a) (λ · a + μ · b) · (ν · a + τ · b); b) projection (ν · a + τ · b) to b; a) cos (a + τ · b).
Given: α = 5; β = -2; γ = 3; δ = 4; k = 2; ℓ = 5; φ = π / 2; λ = 2; μ = 3; ν = 1; τ = - 2.
№ 2.17. From the coordinates of points A; B and C for the indicated vectors to find: a) the magnitude of a;
b) the scalar product of a and b; c) the projection of c-vector d; g) coordinates
Points M; dividing the interval ℓ against α :.
Given: A (4; 5; 3); The (-4, 2, 3); C. (5, -6, -2)
№ 3.17. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (7, 2, 1); b (5, 1, -2); c (-3; 4; 5); d (26; 11; 1)