Find a plane containing the point $(-2,3,4)$ and the line of intersection of the planes $-6x - 5y + z = - 3 $ and $-8x + 5y + 3z = -79$
I do not know what to do after you solve for both sets of x,y, and z.
i need help with a calculus 3 problem involving lines and planes in space
-1
$\begingroup$
plane-geometry
1 Answers
1
To write the equation of a plane you need two things. A point on the plane and a normal vector. They give you the point, so you need to find a normal vector.
One way to find the normal vector is to find 3 points in the plain, form two vectors from those points and take the cross product. So you need to find 3 points on the plane. You have one.
The other two could be two points chosen randomly on the line which the plane is supposed to contain. So you need find two points on the line of intersection. You have two equations in three unknowns, so that should be straightforward.