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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 |
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Answer» 3 `(-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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