Final answer:
To find the vector form of the equation of a line that passes through a point and is perpendicular to a plane, we need a normal vector to the plane and a point on the line. The vector form of the equation is r = P + t * N, where r is the position vector, t is a scalar parameter, P is a point on the line, and N is the normal vector to the plane.
Step-by-step explanation:
Vector form of the equation of the line:
To find the vector form of the equation of a line that passes through a point and is perpendicular to a plane, we need a normal vector to the plane and a point on the line. The normal vector to the plane can be found using the coefficients of the general equation of the plane. If the general equation of the plane is Ax + By + Cz + D = 0, then the normal vector is N = (A, B, C). Let's say a point on the line is P = (x₀, y₀, z₀). Then the vector form of the equation of the line passing through P and perpendicular to the plane is r = P + t * N, where r is the position vector and t is a scalar parameter.