Given the three planes $\pi _ { 1 } : - 2 x - 2 y + z = 0$; $\pi _ { 2 } : - 2 x + y - 2 z = 0$ and $\pi _ { 3 } : x - 2 y - 2 z = 0$, it is requested: a) (1 point) Determine the angle formed by the planes pairwise. Determine the intersection of the three planes. b) (1.5 points) Determine the point $P$ in space such that its orthogonal projection onto $\pi _ { 1 }$ is the point $Q _ { 1 } ( 1 / 3,4 / 3,10 / 3 )$ and its orthogonal projection onto $\pi _ { 2 }$ is the point $Q _ { 2 } ( - 1 / 3,8 / 3,5 / 3 )$. Determine the orthogonal projection $Q _ { 3 }$ of the point $P$ onto the plane $\pi _ { 3 }$.
Given the three planes $\pi _ { 1 } : - 2 x - 2 y + z = 0$; $\pi _ { 2 } : - 2 x + y - 2 z = 0$ and $\pi _ { 3 } : x - 2 y - 2 z = 0$, it is requested:
a) (1 point) Determine the angle formed by the planes pairwise. Determine the intersection of the three planes.
b) (1.5 points) Determine the point $P$ in space such that its orthogonal projection onto $\pi _ { 1 }$ is the point $Q _ { 1 } ( 1 / 3,4 / 3,10 / 3 )$ and its orthogonal projection onto $\pi _ { 2 }$ is the point $Q _ { 2 } ( - 1 / 3,8 / 3,5 / 3 )$. Determine the orthogonal projection $Q _ { 3 }$ of the point $P$ onto the plane $\pi _ { 3 }$.