Пошаговое объяснение:
BA = {Ax - Bx; Ay - By; Az - Bz} = {1 - (-3); 2 - 2; -3 - 1} = {4; 0; -4}
BC = {Cx - Bx; Cy - By; Cz - Bz} = {4 - (-3); -1 - 2; 1 - 1} = {7; -3; 0}
|BA| = √(BA²x + B²A2 + BA²z) = √(4² + 0² + 4²) = √(16 + 0 + 16) = √32 = 4√2
|BC| = √(BC²x + BC²y + BC²z) = √(7² + (-3)² + 0²) = √(49 + 9 + 0) = √58
BA*BC = BAx*BCx + BAy*BCy + BAz*BCz = 4*7 + 0*(-3) + 4*0 = 28+0+0 = 28
cos α = (BA*BC ) / |BA||BC| = 28 / (4√2 * √58) = 7√28 / 58
Пошаговое объяснение:
BA = {Ax - Bx; Ay - By; Az - Bz} = {1 - (-3); 2 - 2; -3 - 1} = {4; 0; -4}
BC = {Cx - Bx; Cy - By; Cz - Bz} = {4 - (-3); -1 - 2; 1 - 1} = {7; -3; 0}
|BA| = √(BA²x + B²A2 + BA²z) = √(4² + 0² + 4²) = √(16 + 0 + 16) = √32 = 4√2
|BC| = √(BC²x + BC²y + BC²z) = √(7² + (-3)² + 0²) = √(49 + 9 + 0) = √58
BA*BC = BAx*BCx + BAy*BCy + BAz*BCz = 4*7 + 0*(-3) + 4*0 = 28+0+0 = 28
cos α = (BA*BC ) / |BA||BC| = 28 / (4√2 * √58) = 7√28 / 58