IDZ Ryabushko 2.1 Variant 14
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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 = -2; β = 3; γ = 5; δ = 1; k = 2; ℓ = 5; φ = 2π; λ = -3; μ = 4; ν = 2; τ = 3.
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(10; 6; 3); В( -2;3;5); С(3; –4 ;-6 ); ...
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( 4;2;3 ); b( –3;1;-8); c(2; –4;5); d(-12;14 ;-31).
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 = -2; β = 3; γ = 5; δ = 1; k = 2; ℓ = 5; φ = 2π; λ = -3; μ = 4; ν = 2; τ = 3.
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(10; 6; 3); В( -2;3;5); С(3; –4 ;-6 ); ...
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( 4;2;3 ); b( –3;1;-8); c(2; –4;5); d(-12;14 ;-31).
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