Find a vector parametric equation for a line containing a given point and perpendicular to a given plane

by RoRi

May 30, 2016

Let $L$ be the line which contains the point $(2,1,-3)$ and is perpendicular to the plane given by the equation $4x - 3y + z = 5$ . Find a vector parametric equation for $L$ .

From the Cartesian equation for the plane we have $N = (4,-3,1)$ is a normal vector. So, $L$ is the line through $(2,1,-3)$ which is parallel to $(4,-3,1)$ . Thus, the vector parametric equation for the line is

$X(t) = (2,1,-3) + t(4,-3,1).$

Stumbling Robot

Find a vector parametric equation for a line containing a given point and perpendicular to a given plane

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