Two unit vectors that are normal to the plane

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SUMMARY

The discussion focuses on finding two unit vectors normal to the plane defined by points A(0,-2,1), B(1,-1,-2), and C(-1,1,0). The user successfully calculated the cross product of the position vectors, resulting in the vector 8i + 4j + 4k. To obtain the unit vector, they divided this vector by its magnitude. The user inquired about generating a second unit vector, questioning whether to simply reverse the direction of the first unit vector.

PREREQUISITES
  • Understanding of vector operations, specifically cross products.
  • Familiarity with unit vectors and their properties.
  • Knowledge of calculating vector magnitudes.
  • Basic concepts of 3D geometry and planes.
NEXT STEPS
  • Study the properties of cross products in vector mathematics.
  • Learn how to calculate the magnitude of a vector in three-dimensional space.
  • Explore the concept of normal vectors in the context of planes.
  • Investigate the geometric interpretation of reversing vector directions.
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Students studying linear algebra, geometry enthusiasts, and anyone learning about vector calculus and its applications in 3D space.

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Homework Statement


Find two unit vectors that are normal to the plane determined by the points A(0,-2,1), B(1,-1,-2), and C(-1,1,0)

I found the cross-product of the two position vectors then i got 8i+4j+4k then i divided that by the magnitude to get the unit vector but how do i find the other one? can i just add a coefficient in front of the unit vector?
 
Last edited:
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Take the opposite direction.
 

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