Example 9: Line Perpendicular to a Plane

Find the line L through the point P(1, 2, 3) which is perpendicular to the plane 3x - 4y + z = 10.

The plane has the normal vector N = 3i - 4j + k. Therefore N is a direction vector of L, and L has the vector equation

X = P + tN,

X = i + 2j + 3k + t(3i - 4j + k)

(see Figure 10.5.11).

Figure 10.5.11