The distance of line 3y−2z−1=0=3x−z+4 from the point (2,−1,6) is:
(A) 2√6
(B) √26
(C) 2√5
(D) 4√2
Solution
We have, 3x−z+4=0 or z=3x+4
& 3y−2z−1=0 or 3y−2(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=(t−2)2+(2t+3+1)2+(3t+4−6)2=14t2+24
Minimum d = Required answer = √24=2√6 when t = 0.
Answer: (A)