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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 point A is `(p,q,r)` then `p-q+r` isA. 3B. `-3`C. `4`D. `-4` |
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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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