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IDZ Ryabushko 2.1 Variant 22
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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 = -7; β = 2; γ = 4; δ = 6; k = 2; ℓ = 9; φ = π/3; λ = 1; μ = 2; ν = -1; 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 (–5 ; –2 ; – 6 ) ; В ( 3 ; 4 ; 5 ) ; С ( 2 ; – 5 ; 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( 7;2;1); b( 3;–5;6 ); c(–4;3;–4 ); d(–1; 18; – 16 ).
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