I am looking for the equation of a plane which passes through the x-axis and the point A(3,1,-4), and am confused as to how to go about solving the problem. I am thinking that I can take two random points that cross the x-axis, and then take the cross product of two vectors created by the three points. From that I would get the vector perpendicular to the plane, and then I would be able to get the equation of the plane. Would my approach be correct, or is there a simpler way of finding the equation of the plane?
[Math] Find the equation of plane through the x-axis and another point.
linear algebra
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Best Answer
The general equation for a plane which contains the $x$-axis is $y+cz=0$ for some constant $c$. For the plane to contain the point $(3,1,-4)$ you need to have $1-4c=0$.