MHB How Can We Geometrically Describe Vectors Orthogonal to the Vector $(-4,1,-3)$?

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Vectors orthogonal to the vector $(-4,1,-3)$ can be geometrically described as lying in a plane that is perpendicular to this vector and passes through the origin. The equation of this plane is given by $-4x + y - 3z = 0$. This equation represents all points (x, y, z) that satisfy the orthogonality condition with respect to the given vector. Understanding this geometric representation is crucial for visualizing vector relationships in three-dimensional space. The discussion highlights the importance of planes in vector analysis.
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Hey!

How could we describe geometrically the vectors that are orthogonal to the Vector $(-4,1,-3)$ ?
 
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mathmari said:
Hey!

How could we describe geometrically the vectors that are orthogonal to the Vector $(-4,1,-3)$ ?

Hey mathmari! (Smile)

It's the plane perpendicular to the vector that contains the origin.
Its equation is:
$$(x,y,z)\cdot (-4,1,-3)=0 \quad \Leftrightarrow \quad -4x+y-3z=0$$
(Mmm)
 
Thank you very much! (Mmm)
 

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