EasyMathematicsHigh School (11–12)Vectors and Three-Dimensional Geometry › Three-Dimensional GeometryNumericalBoard ExamA-LevelIB
A flat roof panel passes through the point A(2, -1, 4), with coordinates in metres, and a…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A flat roof panel passes through the point , with coordinates in metres, and a vertical-looking support rod, which is the normal of the panel, points along . The origin is a reference point on the ground. Write the equation of the panel in the form . Find , the distance of the panel from the origin, and the point where the panel meets the -axis.
Need a reminder? The key ideaShow
A plane with normal through the point is . Through three points, a normal is . The distance of from the origin 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. The constant. . The plane is .
Step 2. The distance from the origin. The length of the normal is . The distance is metres.
Step 3. The -axis. Put . Then and metres.
Answer: , the distance is about metres, and the panel meets the -axis at metres.
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