Atividade A3 - Álgebra Linear Computacional

w = \\begin{pmatrix} 1 \\ 1 \\ 1 \\end{pmatrix} = \\begin{pmatrix} -1 \\ -1 \\ -3 \\end{pmatrix} + \\begin{pmatrix} 2 \\ -2 \\ 0 \\end{pmatrix} + \\mathbf{k}\;: w = (2, -2, 0) Cos (θ) = \\frac{\\mathbf{u} \\cdot \\mathbf{v}}{|\\mathbf{u}||\\mathbf{v}|} = \\frac{(1,1,1) \\cdot (1,1,3)}{\\sqrt{1+1+1} \\cdot \\sqrt{1+1+3}} = \\frac{5}{\\sqrt{33}} \\approx 0.87\ncos^{-1}(0.87) = 29.5^\\circ C = (1, 1, 3)\nD = (2, -2, 0)\nα = ∠(B, A, C)\n= 28°\nβ = ∠(C, A)\n= -90°\nγ = ∠(D, A, B)\n= 90°\nPolígono\nArea w = u × v = (2,0)\nA = \\frac{1}{2} |2,-2,0| - \\frac{1}{2} |2,83 ≈ 1,41