The distance of line 3y2z1=0=3xz+4 from the point (2,1,6)=?

The distance of line 3y2z1=0=3xz+4 from the point (2,1,6) is:

(A) 26
(B) 26
(C) 25
(D) 42

Solution

We have, 3xz+4=0 or z=3x+4
& 3y2z1=0 or 3y2(3x+4)1=0 or y=2x+3

Any point (x,y,z) on the line (t,2t+3,3t+4)

Let d be the distance between (2,1,6) & (t,2t+3,3t+4)

Then, d2=(t2)2+(2t+3+1)2+(3t+46)2=14t2+24

Minimum d = Required answer = 24=26 when t = 0.

Answer: (A)

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