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IDZ Ryabushko 2.1 Variant 10
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Uploaded: 09.04.2024
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Product description
No.1 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) the projection (ν · a + τ · b) on b; c) cos (a + τb).
Given: α = 5; β = -3; γ = 4; δ = 2; k = 4; ℓ = 1; φ = 2π/3; λ = 2; μ =-1/2; ν = 3; τ = 0.
No.2 According to the coordinates of points A; B and C for the indicated vectors find: a) the module of the vector a;
b) the scalar product of the vectors a and b; c) the projection of the vector c onto the vector d; d) coordinates
points M; dividing the segment ℓ with respect to α :.
Given: А(0; 2; 5); В( 2;-3;4); С(3;2;-5); ...
No.3 Prove that the vectors a; b; c form a basis and find the coordinates of the vector d in this basis.
Given: a(3;-1;2); b(–2;3;1); c(4;–5;-3); d(-3;2;-3).
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