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Find a point on the line (x+2)/3 = (y+1)/2 = (z-3)/2 at a distance of 3*sqrt(2) from the point (1,2,3).

Find a point on the line (x+2)/3 = (y+1)/2 = (z-3)/2 at a distance of 3*sqrt(2) from the point (1,2,3).

Grade:12

1 Answers

Likith Narayan ss
19 Points
10 years ago

 (x+2)/3 = (y+1)/2 = (z-3)/2=k(let)

(x+2)/3=k and (y+1)/2=k and  (z-3)/2=k

given x=3k-2,y=2k-1,z=2k+3 given(x,y,z) is at a distance of 3sqrt2 from(1,2,3)

sqrt(3-3k)+(3-2k)2+(-2k)2=3sqrt2

squaring on both sides

9+9k2-18k+4k2-12k+9+4k2=18

17k2-30k =0

k(17k-30)=0

k=0 ork=17/30

substitute k=0 x=-2,y=-1,z=3 therefore point is (-2,-1,3)

also find point for k=17/30

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