spain-selectividad 2020 QB.3

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2 marks Vectors 3D & Lines Multi-Part 3D Geometry Problem

For the parallelogram $ABCD$, the consecutive vertices $A(1,0,-1)$, $B(2,1,0)$ and $C(4,3,-2)$ are known. Find:\ a) (1 point) Calculate an equation of the line that passes through the midpoint of segment $AC$ and is perpendicular to segments $AC$ and $BC$.\ b) (1 point) Find the coordinates of vertex $D$ and the area of the resulting parallelogram.\ c) (0.5 points) Calculate the cosine of the angle formed by vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$.

For the parallelogram $ABCD$, the consecutive vertices $A(1,0,-1)$, $B(2,1,0)$ and $C(4,3,-2)$ are known. Find:\
a) (1 point) Calculate an equation of the line that passes through the midpoint of segment $AC$ and is perpendicular to segments $AC$ and $BC$.\
b) (1 point) Find the coordinates of vertex $D$ and the area of the resulting parallelogram.\
c) (0.5 points) Calculate the cosine of the angle formed by vectors $\overrightarrow{AB}$ and $\overrightarrow{AC}$.

Paper Questions

QA.1 QA.2 QA.3 QA.4 QB.1 QB.2 QB.3 QB.4