spain-selectividad 2018 Q3

spain-selectividad · Other · selectividad__madrid_matematicas-II_ordinaria 2.5 marks Vectors 3D & Lines Multi-Part 3D Geometry Problem
Given the planes $\pi _ { 1 } \equiv 4 x + 6 y - 12 z + 1 = 0 , \pi _ { 2 } \equiv - 2 x - 3 y + 6 z - 5 = 0$, it is requested:
a) (1 point) Calculate the volume of a cube that has two of its faces in these planes.
b) (1.5 points) For the square with consecutive vertices ABCD , with $\mathrm { A } ( 2,1,3 )$ and $\mathrm { B } ( 1,2,3 )$, calculate the vertices C and D , knowing that C belongs to the planes $\pi _ { 2 } \mathrm { and } \pi _ { 3 } \equiv x - y + z = 2$.
Given the planes $\pi _ { 1 } \equiv 4 x + 6 y - 12 z + 1 = 0 , \pi _ { 2 } \equiv - 2 x - 3 y + 6 z - 5 = 0$, it is requested:

a) (1 point) Calculate the volume of a cube that has two of its faces in these planes.

b) (1.5 points) For the square with consecutive vertices ABCD , with $\mathrm { A } ( 2,1,3 )$ and $\mathrm { B } ( 1,2,3 )$, calculate the vertices C and D , knowing that C belongs to the planes $\pi _ { 2 } \mathrm { and } \pi _ { 3 } \equiv x - y + z = 2$.
Paper Questions