spain-selectividad 2020 QA.3

spain-selectividad · Other · selectividad__madrid_matematicas-II_extraordinaria 2 marks Vectors 3D & Lines Multi-Part 3D Geometry Problem
Given the point $P(3,3,0)$ and the line $r \equiv \frac{x-2}{-1} = \frac{y}{1} = \frac{z+1}{0}$, find:\ a) (0.75 points) Write the equation of the plane that contains point $P$ and line $r$.\ b) (1 point) Calculate the point symmetric to $P$ with respect to $r$.\ c) (0.75 points) Find two points $A$ and $B$ on $r$ such that triangle $ABP$ is right-angled, has area $\frac{3}{\sqrt{2}}$ and the right angle is at $A$.
Given the point $P(3,3,0)$ and the line $r \equiv \frac{x-2}{-1} = \frac{y}{1} = \frac{z+1}{0}$, find:\
a) (0.75 points) Write the equation of the plane that contains point $P$ and line $r$.\
b) (1 point) Calculate the point symmetric to $P$ with respect to $r$.\
c) (0.75 points) Find two points $A$ and $B$ on $r$ such that triangle $ABP$ is right-angled, has area $\frac{3}{\sqrt{2}}$ and the right angle is at $A$.