EasyMathematicsHigh School (11–12)Vectors and Three-Dimensional Geometry › Introduction to Three-Dimensional GeometryNumerical
In a large hall the origin is at the foot of a pillar, the xy-plane is the floor and the z-axis…
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 large hall the origin is at the foot of a pillar, the -plane is the floor and the -axis runs up the pillar. A balloon floats at the point , with distances in metres. Find the distance of the balloon from the base of the pillar, which is the origin. Then find its distance from the -axis, which is the line of the pillar.
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 origin. .
Step 2. From the -axis. .
Check. The distance from the axis is shorter than the distance from the origin, as it should be.
Answer: the balloon is from the origin and from the -axis.
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