Find Vector Perpendicular to Plane

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SUMMARY

The discussion focuses on finding a vector perpendicular to a plane defined by the points P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2) using the vector product. The vectors $\vec{PQ}$ and $\vec{PR}$ are calculated as $\vec{PQ} = (1, 1, -2)$ and $\vec{PR} = (2, -1, -1)$. The cross product $\vec{PQ} \times \vec{PR}$ is established as the method to derive the perpendicular vector. The determinant method for calculating the cross product is also referenced.

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  • Understanding of vector operations, specifically cross product
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  • Knowledge of determinants and matrix representation
  • Basic skills in vector notation and manipulation
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brinlin
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Find a vector that is perpendicular to the plane passing through the points P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2).
 
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vector product yields a vector perpendicular to two vectors ...

$\vec{PQ} \times \vec{PR}$
 
I'm sorry I don't really understand.
 
brinlin said:
I'm sorry I don't really understand.

you don't understand, or you don't know what a vector product is and how to calculate it?

$\vec{PQ} = (1,1,-2)$
$\vec{PR} = (2,-1,-1)$

$ \vec{PQ} \times \vec{PR} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 1& 1 & -2 \\ 2 &-1 &-1 \\ \end{vmatrix} $
 

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