The discussion focuses on finding the vector equation of a line in three-dimensional space that passes through the point P = (-1, 3, 0) and is orthogonal to the plane defined by the equation 3x - z = 2. The normal vector of the plane, derived from its equation, is (3, 0, -1). The equation (P - P0)·n = 0 is applicable, where P0 is the given point and n is the normal vector. The challenge lies in determining the intersection point between the vector and the plane, which is essential for fully specifying the line's equation.
PREREQUISITESStudents studying geometry, particularly those tackling vector equations and plane intersections, as well as educators looking for examples of orthogonal relationships in three-dimensional space.
miniake said:Homework Statement
Find the vector equation of line in three dimensional space that contains the point
P = (-1,3,0) and is orthogonal to the plane 3x - z = 2.
Homework Equations
The attempt at a solution
can I use the equation of (P-P0)n = 0 , in this question?
Since the only problem is, I don't know how to find the intersection point between the vector and the plane.
Any hints? Thanks.