To find the point of intersection, we need to set the parametric equations of the line equal to the equation of the plane. This will give us a system of equations that we can solve for the values of the parameters, which will give us the coordinates of the point of intersection.
The necessary conditions for a line in parametric form to intersect a plane are that the line must lie in the plane or be parallel to it. In addition, the line must not be contained within the plane.
Yes, a line in parametric form can intersect a plane at more than one point. This can happen if the line lies within the plane or if the line is parallel to the plane and intersects it at multiple points along its direction.
If the vector components of the line's direction are proportional to the coefficients of the plane's equation, then the line and plane are parallel. Alternatively, if the cross product of the direction vector and the normal vector of the plane is equal to the zero vector, then the line and plane are parallel.
Yes, a line in parametric form and a plane can be perpendicular. This occurs when the direction vector of the line is parallel to the normal vector of the plane. In this case, the dot product of the direction vector and the normal vector will equal zero, indicating a perpendicular relationship.