IDZ Ryabushko 2.1 Variant 20
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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 = 3; β = -5; γ =-2; δ = 3; k = 1; ℓ = 6; φ = 3π/2; λ = 4; μ = 5; ν = 1; τ = -2.
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(5;4;4 ); В(–5;2;3);С(4;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(11;1;2 ); b(–3;3; 4); c(–4;–2; 7 ); d(–5; 11;–15 ).
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 = 3; β = -5; γ =-2; δ = 3; k = 1; ℓ = 6; φ = 3π/2; λ = 4; μ = 5; ν = 1; τ = -2.
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(5;4;4 ); В(–5;2;3);С(4;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(11;1;2 ); b(–3;3; 4); c(–4;–2; 7 ); d(–5; 11;–15 ).
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