What is the shortest distance of the plane from the origin in ?
In the coordinates, the centroids of the 3 faces of a cuboid are located at points , and , where each side is parallel to one of the axes.
What is the volume of this cuboid?
Let be the triangle with vertices , , and .
Line goes through the origin and intersects perpendicularly in point .
Determine the distance .
The graph intersects with the graph , where and are real numbers, such that the intersected points form a parabola with the point as its vertex.
What is the value of ?
Find the coordinates of the point where the line through and crosses the -plane
Submit answer as the sum of the coordinates.