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A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A normal vector, n, to this plane is (2,-3,1). Find the scalar equation.

A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A normal vector, n, to this plane is (2,-3,1). Find the scalar equation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A point P (3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+ Cz + D = 0. A normal vector, 7, to this plane is (2, -3,1). Find the scalar equation. How many solutions are there between the plane P₁: (x, y, z) =(4,-3,-1) + s(1, -3,1)+t(2,4,-3) and the line L₁: (x, y, z)=(3,1-2) +k(-1,-1,1)? If there is/are solutions, find the value of the solution(s).
Transcribed Image Text:A point P (3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+ Cz + D = 0. A normal vector, 7, to this plane is (2, -3,1). Find the scalar equation. How many solutions are there between the plane P₁: (x, y, z) =(4,-3,-1) + s(1, -3,1)+t(2,4,-3) and the line L₁: (x, y, z)=(3,1-2) +k(-1,-1,1)? If there is/are solutions, find the value of the solution(s).
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