Asked by Kean
(a) Give an example of three planes in R^3 that have a common line of intersection. Justify your answer.
(b) Give an example of three planes in R^3 that intersect in pairs but have no common point of intersection. Justify your answer.
(c) Give an example of three planes in R^3 that intersect in a single point. Justify your answer.
(b) Give an example of three planes in R^3 that intersect in pairs but have no common point of intersection. Justify your answer.
(c) Give an example of three planes in R^3 that intersect in a single point. Justify your answer.
Answers
Answered by
oobleck
It should be easy to come up with (c)
In fact, most of your exercises will intersect at a point.
Now just adjust one of the planes so that it works for (a) and (b)
I'm sure your text has examples of such situations.
In fact, most of your exercises will intersect at a point.
Now just adjust one of the planes so that it works for (a) and (b)
I'm sure your text has examples of such situations.
Answered by
Reiny
Here is an excellent video, with diagrams and example set of equations.
There are actually 3 videos, they should run into each other.
https://www.youtube.com/watch?v=duFRYId7kNU
There are actually 3 videos, they should run into each other.
https://www.youtube.com/watch?v=duFRYId7kNU
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