- #1
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SUMMARY
The discussion centers on finding the equation of a plane given three points, specifically arriving at the equation 2x + y + 7z = -3. A participant expresses confusion over their incorrect calculations, particularly in computing the cross-product necessary for determining the normal vector of the plane. The error identified involves miscalculating components of the cross-product, leading to an incorrect normal vector and, consequently, the wrong plane equation.
PREREQUISITES- Understanding of vector mathematics
- Familiarity with cross-product calculations
- Knowledge of plane equations in three-dimensional space
- Basic algebra skills for manipulating equations
- Review vector cross-product calculations in 3D geometry
- Study the derivation of plane equations from normal vectors
- Practice solving problems involving multiple points in three-dimensional space
- Explore resources on linear algebra concepts related to planes and vectors
Students studying geometry, particularly those tackling problems involving planes and vectors, as well as educators looking for examples of common mistakes in vector calculations.
- #2
mfb
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Can you explain what you calculated there?
- #3
SammyS
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You calculated the cross-product incorrectly.uzman1243 said:Homework Statement
[IMG ]https://www.physicsforums.com/attachment.php?attachmentid=68806&stc=1&d=1397897233[/PLAIN]
Homework Equations
N/A
The Attempt at a Solution
The problem is that I don't get the right answer which is:
2x + y + 7z = -3.
Can you please help me find where I went wrong?
##\left( -2 + 0 \right)\hat i \ne 0\hat i ##
##\hat k \left( \ (1) (-3) - (-2)(-2)\ \right)\ne \hat k \left(-3 + 4 \right)##
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