SOLUTION: Find points on the line with parametric equations x=2-t,y=3+2t and z=1+t which are 5√3 units from the point(1,0,-2)

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Question 1130911: Find points on the line with parametric equations x=2-t,y=3+2t and z=1+t which are 5√3 units from the point(1,0,-2)
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We want the square of the distance between (2-t,3+2t,1+t) and (1,0,-2) to be (5*sqrt(3))^2 = 75:

%28%282-t%29-1%29%5E2%2B%28%283%2B2t%29-0%29%5E2%2B%28%281%2Bt%29-%28-2%29%29%5E2+=+75
%281-t%29%5E2%2B%283%2B2t%29%5E2%2B%283%2Bt%29%5E2+=+75
%28t%5E2-2t%2B1%29%2B%284t%5E2%2B12t%2B9%29%2B%28t%5E2%2B6t%2B9%29+=+75
6t%5E2%2B16t-56+=+0
3t%5E2%2B8t-28+=+0
%283t%2B14%29%28t-2%29+=+0
t+=+-14%2F3 or t+=+2

(a) if t=2, then (2-t,3+2t,1+t)=(0,7,3)
(b) if t = -14/3, then (2-t,3+2t,1+t) = (20/3,-19/3,-11/3)

ANSWERS: the two points on the line with the given parametric equations that are a distance of 5*sqrt(3) from (1,0,-2) are (0,7,3) and (20/3,-19/3,-11/3).