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What is the shortest distance between P = (1, 5, 2) and the line L : (x,y,z) = (3, -1 , 1) + t (4, -3, 2) ?
What is the shortest distance between P = (1, 5, 2) and the line L : (x,y,z) = (3, -1 , 1) + t (4, -3, 2) ?
Is there a formula for this ??
1 Answer
- Anonymous7 years agoFavorite Answer
Let Q = (3 - 4t, -1 - 3t, 1 +2t) be a point on L
The square of the distance between P and that point on L is
d(t) = (1 - 3 - 4t)^2 + (5 +1 + 3t)^2 + (2 - 1 - 2t)^2
Just find where d(t) has a minimum. You can take the derivative if you've had calculus, or just put it in standard form of a parabola if you've only had algebra,
Then d(t) is your answer, and you can use t to find the point on L.