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Solved: Properties of planes Find the points at which the
Chapter 12, Problem 19E(choose chapter or problem)
Properties of planes Find the points at which the following planes intersect the coordinate axes and find equations of the lines where the planes intersect the coordinate planes. Sketch a graph of the plane.
3x-2y+z=6
Questions & Answers
QUESTION:
Properties of planes Find the points at which the following planes intersect the coordinate axes and find equations of the lines where the planes intersect the coordinate planes. Sketch a graph of the plane.
3x-2y+z=6
ANSWER:Solution 19E
Step 1 of 5:
In this problem we need to find the points at which the plane 3x - 2y +z = 6 intersects the coordinate axes and we have to find an equations of the lines where the planes intersects the coordinate axes.
The given plane (P) is : 3x - 2y +z = 6.
Now let us find the x-intercept:
Let us consider ( x , y , z) be the intersection point of plane and x -axis .
We know that on x -axis y and z coordinates are zero.
Substitute y = z = 0 into the equation of P we get :
3x -2(0) +(0) = 6
Therefore , P intersects the x-axis at (2 , 0 ,0).