RAP IDZ 2.1 option 22

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DHS - 2.1

№ 1.22. 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 = -7; β = 2; γ = 4; δ = 6; k = 2; ℓ = 9; φ = π / 3; λ = 1; μ = 2; ν = -1; τ = 3.

№ 2.22. 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 (-5, -2, - 6); In (3; 4; 5); C. (2 - 5; 4); .......

№ 3.22. 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 (3, -5, 6); c (-4; 3; 4); d (-1; 18 - 16)

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