IDZ Ryabushko 2.1 Variant 16
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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 = -5; β = 3; γ =2; δ = 4; k = 5; ℓ = 4; φ = π; λ = -3; μ = 1/2; ν = 1; τ = 1.
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(–2;3;–4); В(3;–1;2); С(4;2;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;6 ); b(–3;4;–5); c(1;–7;2); d(–2;17;5).
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 =2; δ = 4; k = 5; ℓ = 4; φ = π; λ = -3; μ = 1/2; ν = 1; τ = 1.
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(–2;3;–4); В(3;–1;2); С(4;2;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;6 ); b(–3;4;–5); c(1;–7;2); d(–2;17;5).
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