Question

Find an equation of the plane. The plane through the point (1,0,−3) and perpendicular to the line x=1−2t,y=5−4t,z=9+2t

___x+____y+______z+0

Answer 1

To find the equation of the plane through a given point and perpendicular to a given line, we need to use the point-normal form of the equation of a plane.

Step-by-step explanation:

To find an equation of the plane, we need a point on the plane and a vector that is perpendicular to the plane. We are given the point (1,0,-3) and we can find a vector perpendicular to the plane by taking the direction vector of the line given, which is (-2,-4,2). The equation of the plane is then given by:

(x-1)(-2) + (y-0)(-4) + (z+3)(2) = 0

Simplifying this equation, we get:

-2x - 4y + 2z + 6 = 0