IDZ Ryabushko 2.1 Variant 19
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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 = 4; β = -5; γ = -1; δ = 3; k = 6; ℓ = 3; φ = 2π/3; λ = 2; 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(–4; –2; –5 ); В(3;7;2); С( 4;6; –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( 5;3;2); b( 2;–5; 1); c(–7;4;–3 ); d( 36; 1; 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 = 4; β = -5; γ = -1; δ = 3; k = 6; ℓ = 3; φ = 2π/3; λ = 2; 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(–4; –2; –5 ); В(3;7;2); С( 4;6; –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( 5;3;2); b( 2;–5; 1); c(–7;4;–3 ); d( 36; 1; 15 ).
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