GEOMETRIA x=z+2 190 P 2 ; __ ; 0 ; ) r: x+y=0 {y + z = 1 191 P( 4 ; 0 ; 1) r: 2x + 2y + 2z 6 = 0 {x y z 1 = 0 192 P(1 ; 1 ; 1); r: {x + y + z = 0 ( 1 2 _1_ [{y = z + 2 ] x = 4 [y = z + 1 ] x z=0 x=z [{y = 2z + 3] SFIDA Dati i punti A( 2 ; 3 ; 1), B(3 ; 0 ; 1), C(2; 2 ; 3), determinare l equazione della retta r passante per [Esame di Stato 2017] [ ] A e per B e l equazione del piano perpendicolare a r e passante per C. 193 194 SFIDA Dati i punti A( 2 ; 0 ; 1), B(1 ; 1 ; 2), C(0 ; 1 ; 2), D(1 ; 1 ; 0), determinare l equazione del piano passante per i punti A, B, C e l equazione della retta passante per D e perpendicolare al piano . [Esami di Stato Sess. Straordinaria 2016] [ ] PRACTICE WITH CLIL Planes in space Two planes and are given in space, respectively of equation: : x 3y + z 5 = 0 and : x + 2y z + 3 = 0 After having determined the parametric equation of the straight line r identified by them, verify that it belongs to the plane of equation 3x + y z + 1 = 0. [2015 A-levels exam at scientific high schools] Guided solution The two planes intersect because the coefficients of the corresponding variables (x ; y ; z) do not have the same ......... 1 1 ratio (_ _ _) and the straight line r = is represented by the ................................. made of the equations ......... 2 ......... x 3y + z 5 = 0 of the two planes r: which, once its variables x and y are explicitly expressed, we can rewrite { x + 2y z + 3 = 0 as: 1 = .................. z + _ 5 r: 2 y = _ z + .................... 5 x To verify that the straight-line r belongs to the plane, it is sufficient to replace the variables x, y, z of the .................... ............. with the respective expressions of the .................................; we expect to get an ................................. 3x + y z + 1 = 0 3 ....................... ..................................................................... + =0 ....................... ..................................................................... Being an ................................. the straight line belongs to the plane. 412 z+1=0 .......................................................................... =0