Two flat plates are parallel, and they lie in the planes 2x - 2y + z = 8 and 2x - 2y + z = -4, with…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two flat plates are parallel, and they lie in the planes and , with coordinates in metres. A small sensor sits at , between the planes. Find the distance of from the first plane, the coordinates of the foot of the perpendicular from to the first plane, and the distance between the two plates.
Need a reminder? The key ideaShow
The distance of from is . Two planes meet in a line with direction .
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. The distance. . The length of the normal is , so the distance is metres.
Step 2. The foot. . Check: .
Step 3. The plates. The coefficients are the same. The distance is metres.
Answer: metres, the foot , and metres between the plates.
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