If the lines x-1 /2 = y+1 /3 =z-1 /4 and x-3 /1 =y-k /2 =z/1 intersect , then the value of k s

Answers (1)

Solution:  Given , 

            \ \ L_1: fracx-12=fracy+13=fracz-14 = lambda \ \ L_2:fracx-31=fracy-k2=fracz1=mu

 General point on the given line L_1:(2lambda+1,3lambda-1,4lambda+1)  and 

   L_2:(3+mu,k+2mu,mu)  Since the above lines intersect  then 

                       \ \ 2lambda+1=3+mu hspace1cm........(1)\ \ 3lambda-1=2mu+k hspace1cm........(2)\ \ mu=4lambda+1 hspace1cm.........(3)

 Sloving   (1) and  (2) and putting the value of  lambda  and mu in (2)

                         k=frac92   

                   

 

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