EasyMathematicsHigh School (11–12)Vectors and Three-Dimensional Geometry › Three-Dimensional GeometryNumericalA-LevelIB
A ceiling in a hall is tilted and lies in the plane 4x - 4y + 7z = 7, with coordinates in metres…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A ceiling in a hall is tilted and lies in the plane , with coordinates in metres. A lamp hangs at the point . Find the value of at , and the shortest distance from the lamp to the ceiling.
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 value. .
Step 2. The length of the normal. .
Step 3. The distance. metres.
Answer: and metres.
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