# 3awar khan linear dependence and coplanarity 7 1 34

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3awarKhanLinearDependenceandCoplanarity7)[1,-3,4][4,2,-2][3-2,3]-341-3R→[-3/8,14]-[3-2,3]2-242[-2,18,ly]-b-36+42-2×+184+142+1=02-242-233-2[2,-18,-14]These3vectorallCopkrnerSinceCrossproductoftwovectorsisthenumbervectorofanyathezvectorcrosproductChannel)
April1620173awarKhanLinearDependenceandCoplanarity8a)[2/3,5]To:b,]eo"near8b)a-C2,3,I]CoplahorI[1,6/2]3I23RtoG216Co,-3,9)in0-34+92=0fory=1-3+92=0gz=32-=13E[0,1,tz]X3E[0,3,l]L
April1620173awarKhanLinearDependenceandCoplanarity8C)[4,6,12][3/1,0][0,2,3]9)AC3,1,4)BC7,-2,9)C(0,8/2)DC8,2,12)BE=C-7,10,-7)ATXBZ=[24,7,-19]normalforpkne292+7y-192td=OCartesianearSobanypointfromAta29(3)+74)-Hcu)+d=087+776td=o18td=ode-18
April1620173awarKhanLinearDependenceandCoplanarity9)NeedD29xtty192-18=0SubinpointD29(8)+7(2)-14(12)-18=0232+14-228-18=00=04pointsCoplanarSinceSobbed4thpointinCortesrahegeetronOfplaneandgotCorrectSolution
April1620173awarKhanLinearDependenceandCoplanarityio)8,=28,tsvz52=52t28383=T-753[(XXWI)]t[(4)(wz)]t[czxws,]to[A)(25,tsuz)]tfilkvzt25)]take-7833=0.'2k)ytscxsuztYJzt2yJ3t-Zu,-7253[(2×-2×0,)]tEx+4)CJz)]tC2y-72×831=0doSinceJ,8z83notcoplanerthereforCoefficientOf0,8203mustbe0i.