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Find the equations of the lines of greatest slope and least slope on the plane $3x-4y+5z-5=0$ drawn through the point $(1,2,2)$ given that the plane $4x-5y+6z-6=0$ is horizontal.

I do not need the solution of the problem rather I am unable to understand the following

  1. What is meant by lines of greatest slope and least slope on the plane? Please explain in details, if possible, graphically.

  2. Why the plane $4x-5y+6z-6=0$ is assumed as horizontal?

I shall be very happy if someone be kind enough to help me by providing the above information so that I can understand the problem and solve.

EDIT:

I understand about lines of greatest slope. Please help me to solve lines of least slope.

user1942348
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    For the first part of your first question, you are welcome to visit my answer in http://math.stackexchange.com/questions/1123724/what-is-the-line-of-greatest-slope-on-a-plane/1123820#1123820 – Mick Apr 14 '16 at 08:58
  • @Mick Really nice explanation for the first. May I get an explanation/definition for the 2nd, the least slope. – user1942348 Apr 14 '16 at 09:15
  • “Least slope” is a term that I have never come across. It probably means, according to my diagram, the slope of the line along AQ. But the location of Q is questionable. It could also mean the "inclined" plane is horizontal such that the slope is zero and is therefore the least. – Mick Apr 14 '16 at 09:26
  • For the second question, WLOG, any plane can be used as reference such that it can be assumed to be horizontal. Just like in proving a target quadrilateral is a parallelogram, we have the right to assume one of the vertices is right at O(0, 0) to simplify our discussion a little bit. – Mick Apr 14 '16 at 09:33

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