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Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and perpendicularly intersects with the plane 3x+5y+4z=487. Q2: Solve the following differential equation in two ways. (2xy + x²)dx + (x² + y² )dy = 0

Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and perpendicularly intersects with the plane 3x+5y+4z=487. Q2: Solve the following differential equation in two ways. (2xy + x²)dx + (x² + y² )dy = 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 17RE
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Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and perpendicularly intersects with the plane 3x+5y+4z=487. Q2: Solve the following differential equation in two ways. (2xy + x?)dx + (x² + y²)dy = 0 Q3: Find the shortest line from a point to a plane, justify your answer by calculations. Hint: you can choose any coordinates of the points and equation of the plane. Q4: Design the biggest box (volume) without cover that made from 6m? of aluminum. Hint: Use Lagrange Multipliers Method
Transcribed Image Text:Q1: Formulate the equation of plane in space that contain two points (2,4,-1) and (1,3,-2) and perpendicularly intersects with the plane 3x+5y+4z=487. Q2: Solve the following differential equation in two ways. (2xy + x?)dx + (x² + y²)dy = 0 Q3: Find the shortest line from a point to a plane, justify your answer by calculations. Hint: you can choose any coordinates of the points and equation of the plane. Q4: Design the biggest box (volume) without cover that made from 6m? of aluminum. Hint: Use Lagrange Multipliers Method
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