- #1

- 410

- 11

I was working on a problem for days.

The problem statement is: "Consider points P(2,1,3), Q(1,2,1), R(-1,-1,-2), S(1,-4,0). Find the shortest distance between lines PQ and RS."

Now, I did the following formula: PS dot (PQ x RS) / magnitude of (PQ x RS). (For skew lines)

Now, I have that

PQ = Q-P = (1,2,1) - (2,1,3) = (-1,1,-2) and

RS = S - R = (1,-4,0)-(-1,-1,-2) = (2,-3,2)

PS = S - P = (1,-4,0) - (2,1,3) = (-1,-5,-3).

PQ x RS = < -1, -5, -3>

Thus, I have PS * (PQ x RS) / | PQ x RS | = <-1,-5,-3> dot <-4,-2,1> (the result of my crossing operation) / sqrt( 4^2 + 2^2 + 1). This results in 11 / sqrt(21).

This is a strange result to me as the book's solution is sqrt(3). Could anyone please give me some feedback as to what I have done (right or wrong)?

Thank you in advance!