Can Someone Verify My Calc 3 Practice Exam Solutions?

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SUMMARY

The forum discussion centers on verifying solutions for a Calculus 3 practice exam. The first problem involves finding the scalar equation of a plane through the point (2,-1,0) and perpendicular to the line defined by the parametric equations x=1-t, y=2+t, z=5, with the proposed solution being -x+y=-3. The second problem requires finding the scalar equation of a plane through the origin and parallel to the plane x+2y-3z=4, with the solution provided as x+2y-3z=0. Both solutions received positive feedback from other forum members.

PREREQUISITES
  • Understanding of scalar equations of planes in three-dimensional space
  • Familiarity with parametric equations of lines
  • Knowledge of vector operations and perpendicularity in geometry
  • Basic skills in solving linear equations
NEXT STEPS
  • Study the derivation of scalar equations of planes from points and normal vectors
  • Learn about the relationship between parametric equations and vector equations
  • Explore examples of parallel and perpendicular planes in three-dimensional geometry
  • Practice solving linear equations involving multiple variables
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Students preparing for Calculus 3 exams, educators teaching multivariable calculus, and anyone seeking to strengthen their understanding of three-dimensional geometry concepts.

wyosteve
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Calc 3 exam tomorrow! Check my solutions please!

Takeing a practice exam but don't have the solutions, anyone who could verify my solutions would be appriciated!

First problem

Find the scalar equation of the plane that passes through (2,-1,0) and is perpendicular to the line x=1-t, y=2+t, z=5

My solution
-x+y= -3

Second problem

Find the scalar equation of the plane that passes through the origin and is parallel to the plane x+2y-3z=4

My solution
x+2y-3z=0

More problems to follow. Thanks in advance for any help!
 
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both look good to me
 


sweet thanks!
 

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