Final answer:
To find the equation of a line perpendicular to the plane and passing through a given point, we need to find the direction vector of the line and use it to write the equation of the line in vector form or scalar form.
Step-by-step explanation:
To find the equation of the line that passes through point P(2, -3, 4) and is perpendicular to the plane with equation 2x - y + 3z = 4, we need to find the direction vector of the line. The direction vector of a line perpendicular to a plane is the normal vector of the plane. For the given plane equation, the normal vector is (2, -1, 3).
Now, we can use the point P(2, -3, 4) and the direction vector (2, -1, 3) to write the equation of the line in vector form as:
r = (2, -3, 4) + t(2, -1, 3) where t is a scalar.
If we want to write the equation of the line in scalar form, we can equate the coordinates of the line with the equation x = 2 + 2t, y = -3 - t, and z = 4 + 3t, where t is a scalar.