IDZ Ryabushko 2.1 Variant 24
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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 = -7; γ = -3; δ = 2; k = 2; ℓ = 11; φ = 3π/2; λ = -3; μ = 4; 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(4;3;2); В(–4; –3; 5);С( 6 ;4; –3 ); ...
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(–2;5; 1); b(3; 2;– 1 ); c( 4; –3; 2 ); d( –4; 22; – 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 = -5; β = -7; γ = -3; δ = 2; k = 2; ℓ = 11; φ = 3π/2; λ = -3; μ = 4; 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(4;3;2); В(–4; –3; 5);С( 6 ;4; –3 ); ...
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(–2;5; 1); b(3; 2;– 1 ); c( 4; –3; 2 ); d( –4; 22; – 13 ).
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