dracolnyte said:parameterized the equation of the line to
x = -1 + 7t
y = 1 - 4t
z = 5 - 5t
The point of intersection between a line and a plane is the single point where the line and the plane intersect each other. It is the point that satisfies both the equation of the line and the equation of the plane.
The point of intersection can be found by solving the equations of the line and the plane simultaneously. This can be done by setting the equations equal to each other and solving for the common variables.
Yes, it is possible for a line and a plane to have more than one point of intersection. This occurs when the line lies within the plane, in which case every point on the line is a point of intersection.
If the line and the plane are parallel, then they will not have any points of intersection. This means that the equations of the line and the plane will not have any common solutions.
Yes, it is possible for a line and a plane to not have any point of intersection. This occurs when the line is parallel to the plane, but not lying within it. In this case, the equations of the line and the plane will not have any common solutions.