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Consider two planes `P_(1):2x-3y++z=-5` and `P_(2):x-4y-14z=5` if a line L whose points `A-=(-7,y_(1),z_(1))` lie on plate `P_(1)` and points `B-=(X_(2),y_(2),z_(2))` and `C-=(x_(3),y_(3),z_(3))` lies on plate `P_(2)` has equation `(x+7)/(a)=(y-y_(1))/(-b)=(z-z_(1))/(c)` where a,b,c `epsilonN` and `a+b+c` is minimum.
Q. The minimum value of `a+b+c` is
A. 3
B. 4
C. 5
D. 6

1 Answer

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Best answer
Correct Answer - D
Line `L:(x+7)/(a)=(y-y_(1))/(-b)=(z-z_(1))/(c)`
`(-7,y,z_(1))` lie on plane `P_(1)`
`implies-3y_(1)+z_(1)=9` ,…(1)
Line L lies on plate `P_(2)`
`impliesa+4b+14c=0` ..(2)
Also `(-7,y_(1),z_(1))` lies on `P_(2)`
`implies-4y_(1)-14z_(1)=12` .. (3)
Form (1) and (3)
Line passes through `(-7,-3,0)`
Least value of a,b,c is `a=2,b=3,c=1`
(from (2))

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