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IDZ Ryabushko 2.1 Variant 25

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IDZ Ryabushko 2.1 Variant 25

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 = -8; γ = -2; δ = 3; k = 4; ℓ = 3; φ = 4π/3; λ = 2; μ = -3; 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; 3); В( 4; 5; 2); С( 2; 7; – 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( 3; 1;2); b( –4; 3; –1 ); c( 2; 3; 4 ); d( 14; 14; 20 ).

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