MediumMathematicsHigh School (11–12)Vectors and Three-Dimensional Geometry › Introduction to Three-Dimensional GeometryNumerical
In a workshop the floor is the plane z = 0 and the ceiling is the plane z = 10, with distances in…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a workshop the floor is the plane and the ceiling is the plane , with distances in metres. The -axis runs along the bottom of one wall. A sensor is fixed at the point . Find the distance of the sensor from the ceiling. Then find its distance from the -axis, which is the line along the bottom of the wall.
Need a reminder? The key ideaShow
The distance from the -axis is , and the other axes follow the same pattern. The distance from the plane is .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. From the ceiling. The ceiling is . The distance is .
Step 2. From the -axis. .
Check. The sensor is above the floor and below the ceiling, and , the height of the room.
Answer: the sensor is from the ceiling and from the -axis.
Discussion (0)
Log in to join the discussion.
Loading…