IDZ Ryabushko 2.1 Variant 28
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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 = 6; β = - 7; γ = -1; δ = -3; k = 2; ℓ = 6; φ = 4π/3; λ = 3; μ = -2; ν = 1; τ = 4.
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 (–3;–5; 6);В(3;5; –4); С( 2; 6;4); ...
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(1; –3; 1); b(–2;–4; 3 ); c(0;–2; 3 ); d(–8; –10; 13 ).
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 = 6; β = - 7; γ = -1; δ = -3; k = 2; ℓ = 6; φ = 4π/3; λ = 3; μ = -2; ν = 1; τ = 4.
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 (–3;–5; 6);В(3;5; –4); С( 2; 6;4); ...
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(1; –3; 1); b(–2;–4; 3 ); c(0;–2; 3 ); d(–8; –10; 13 ).
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