spain-selectividad 2019 Q3

spain-selectividad · Other · selectividad__madrid_matematicas-II_ordinaria 2.5 marks Vectors: Lines & Planes Multi-Step Geometric Modeling Problem
Given the line $r \equiv \frac { x - 1 } { 2 } = \frac { y - 3 } { - 2 } = z$ and the line s that passes through the point $( 2 ; - 5 ; 1 )$ and has direction $( - 1 ; 0 ; - 1 )$, find: a) (1 point) Study the relative position of the two lines. b) (1 point) Calculate a plane that is parallel to r and contains s. c) ( 0.5 points) Calculate a plane perpendicular to the line r and that passes through the origin of coordinates.
Given the line $r \equiv \frac { x - 1 } { 2 } = \frac { y - 3 } { - 2 } = z$ and the line s that passes through the point $( 2 ; - 5 ; 1 )$ and has direction $( - 1 ; 0 ; - 1 )$, find:
a) (1 point) Study the relative position of the two lines.
b) (1 point) Calculate a plane that is parallel to r and contains s.
c) ( 0.5 points) Calculate a plane perpendicular to the line r and that passes through the origin of coordinates.
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