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Question Number 98408 by bemath last updated on 13/Jun/20

Answered by smridha last updated on 13/Jun/20

for L_1 any point (p_1 )can be described as (−1−3t,3+2t,−2+t). for L_2 any point (p_2 ) can be described as (s,7−3s,−7+2s) [s and t are just two parameters] now if p_(1 ) and p_2 became same poit say (p) then we say the two lines are intersecting at point (p) so it is required that −1−3t=s ,3+2t=7−3s,−2+t=−7+2s solving first two we get.. t=−1 and s=2 now put it at 3rd one we get −2−1=−3 and −7+2×2=−3 so the two lines are intersecting at point p and its coordinate is P(2,1,−3) now the equation of plane that containing this two intersecting lines L_(1 ) and L_2 determinant (((x y−7 z+7)),((1 −3 2)),((−3 2 1)))=0 we get: x+y+z=0

forL1anypoint(p1)canbedescribedas(−1−3t,3+2t,−2+t).forL2anypoint(p2)canbedescribedas(s,7−3s,−7+2s)[sandtarejusttwoparameters]nowifp1andp2becamesamepoitsay(p)thenwesaythetwolinesareintersectingatpoint(p)soitisrequiredthat−1−3t=s,3+2t=7−3s,−2+t=−7+2ssolvingfirsttwoweget..t=−1ands=2nowputitat3rdoneweget−2−1=−3and−7+2×2=−3sothetwolinesareintersectingatpointpanditscoordinateisP(2,1,−3)nowtheequationofplanethatcontainingthistwointersectinglinesL1andL2|xy−7z+71−32−321|=0weget:x+y+z=0

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