italy-esame-di-stato 2024 Q3

italy-esame-di-stato · Other · esame-di-stato__matematica Vectors 3D & Lines Line-Plane Intersection
3. In space with orthogonal Cartesian coordinate system $O x y z$, the plane $\pi : 3 x - 2 y + 5 = 0$ is given. -Determine the coordinates of point $H$, the orthogonal projection of $P ( 4,2,1 )$ onto the plane $\pi$; -Determine the intersection of the line $s$ : $\left\{ \begin{array} { l } x - y + 1 = 0 \\ z - 2 = 0 \end{array} \right.$ with the plane $\pi$.
3. In space with orthogonal Cartesian coordinate system $O x y z$, the plane $\pi : 3 x - 2 y + 5 = 0$ is given.\\
-Determine the coordinates of point $H$, the orthogonal projection of $P ( 4,2,1 )$ onto the plane $\pi$;\\
-Determine the intersection of the line $s$ : $\left\{ \begin{array} { l } x - y + 1 = 0 \\ z - 2 = 0 \end{array} \right.$ with the plane $\pi$.\\