MediumMathematicsHigh School (11–12)Vectors and Three-Dimensional Geometry › Introduction to Three-Dimensional GeometryNumerical
A drone reports its position in metres once a second…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A drone reports its position in metres once a second. At second , for , its coordinates are . The origin is the point on the ground below the control tower, and the axes are as in the lesson. On some seconds the drone is exactly on a coordinate plane, and on some seconds it is inside an octant. Find how many of the seven readings are on a coordinate plane. Then find how many readings are in octant IV, where , and .
Need a reminder? The key ideaShow
The three signs of decide the octant. A point on an axis has two zero coordinates, and a point in a coordinate plane has one. The distance of from the -plane is , from the -plane and from the -plane .
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 positions. For to the points are , , , , , and .
Step 2. On a plane. At the -coordinate is . At the -coordinate is . At the -coordinate is . That is readings.
Step 3. Octant IV. For the signs are . For they are , which is octant VI. So readings are in octant IV.
Check. on planes, in octant IV and in octant VI give all readings.
Answer: readings are on a coordinate plane and readings are in octant IV.
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