Find the distance from the point P(1, 4, -3) to the line L: x=2+t, y=-1-t, z=3t by using each of the following methods.

a). If L is a line in 2-space or 3-space that passes through the points A and B, then the distance d from a point P to the line L is equal to the length of the component of the vector that is orthogonal to the vector

b). Show that in 3-space the distance d from a point P to the line L through points A and B can be expressed as

then use this result to find the distance between the point P and line L given at the beginning of this problem.