RAP IDZ 2.1 option 26

DHS - 2.1
№ 1.26. 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 = -3; β = 5; γ = 1; δ = 7; k = 4; ℓ = 6; φ = 5π / 3; λ = -2; μ = 3; ν = 3; τ = -2.
№ 2.26. 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 (6; 4; 5); In (-7, 1, 8) C (2, -2, -7); .......
№ 3.26. Prove that the vector a; b; c and form a basis to find the coordinates of the vector d in this basis.
Given: a (3, -1, 2); b (-2; 4; 1); c (4, -5, -1); d (-5; 11; 1).