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  • Find the value of lambda , if four points with position vector 3i+6j+9k i+2j+3k,2i+3j+k and 4i+6j+(lambda)k are coplanar

Find the value of lambda , if four points with position vector 3i+6j+9k i+2j+3k,2i+3j+k and 4i+6j+(lambda)k are coplanar

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Solution:   Given ,

              vecA=3hati+6hatj+9hatk,hspace0.2cmvecB=hati+2hatj+3hatk\ \Rightarrow vecC=2hati+3hatj+hatk,hspace0.2cmvecD=4hati+6hatj+lambda hatk

       Condition for Coplanar  Rightarrow     left | vecABcdot (vecBC imes vecCD) ight |=0

         Now,        vecAB=vecB-vecA=-2hati-4hatj-6hatk,hspace0.2cmvecBC=hati+hatj-2hatk,hspace0.2cmvecCD=2hati+3hatj+(lambda -1)hatk

      Hence,           eginvmatrix -2 &-4 &-6 \1 &1 &-2 \2 &3 &(lambda -1) endvmatrix=0

           Rightarrow         -2(lambda -1+6)+4(lambda -1+4)-6(3-2)=0   Rightarrow 2lambda =4    Rightarrow lambda =2

                       

Posted by

Deependra Verma

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