( 718, #61) Use the formula to find the distance from the point ( 1, 2, 3 )
to the line x = 2 + t, y = 2 - 3t, z = 5t.

Solution: Using the values t = 0 and t = 1, the two points Q( 2, 2, 0 ) and R( 3, -1, 5) can be computed that lie on the line.

Let a be the vector from Q to R:

a = < 3 - 2, -1 - 2, 5 - 0 > = < 1, -3, 5 >

Let b be the vector from Q to P:

b = < 1 - 2, 2 - 2, 3 - 0 > = < -1, 0, 3 >

The cross product of a and b is:

The distance is:

by: nl