Easy calc 3 question: points on a plane

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SUMMARY

The discussion centers on determining which points P(3,2,1), Q(2,3,1), and R(1,4,1) lie on the plane defined by the equation 3(x-1)+4y-5(z+2)=0. To verify if a point lies on the plane, one must substitute the coordinates of each point into the plane equation. If the equation holds true, that point is on the plane. The conclusion is that substituting the coordinates directly into the equation is the correct approach to solve the problem.

PREREQUISITES
  • Understanding of three-dimensional coordinate systems
  • Familiarity with plane equations in the form Ax + By + Cz + D = 0
  • Basic algebra for substituting values into equations
  • Knowledge of points and vectors in geometry
NEXT STEPS
  • Practice solving plane equations with different points
  • Explore the concept of vector representation in three-dimensional space
  • Learn about the geometric interpretation of planes and points
  • Investigate the implications of points lying on or off a given plane
USEFUL FOR

Students studying calculus, geometry enthusiasts, and anyone looking to strengthen their understanding of three-dimensional planes and point relationships.

meadow
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The question asks:
Which of the points P(3,2,1), Q(2,3,1),R(1,4,1) lie on the plane
3(x-1)+4y-5(z+2)=0?

I know this is a pretty easy problem...but I am drawing a blank on where to start? Should I form vectors from each point ? If so, then what?

A little lost!

Thanks
 
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If the point lies on the plane, then it is a solution to the equation.
 

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