if the lines `(x-1)/2=(y-1)/3=(z-1)/4 and (x-3)/2=(y-k)/1=z/1` intersect then the value of `k` is (a) `1/3` (b) `2/3` (c) `-1/3` (d) `1`A. `(3)/(2)`B. `(9)/(2)`C. `-(2)/(9)`D. `-(3)/(2)`

if the lines `(x-1)/2=(y-1)/3=(z-1)/4 and (x-3)/2=(y-k)/1=z/1` interse

1.	if the lines `(x-1)/2=(y-1)/3=(z-1)/4 and (x-3)/2=(y-k)/1=z/1` intersect then the value of `k` is (a) `1/3` (b) `2/3` (c) `-1/3` (d) `1`A. `(3)/(2)`B. `(9)/(2)`C. `-(2)/(9)`D. `-(3)/(2)`
Answer» Correct Answer - B Since, the lines intersect, therefore they must have a point in common, i.e. `(x-1)/(2)=(y+1)/(3)=(z-1)/(4)=lambeda` and`" "(x-3)/(1)=(y-k)/(2)=(z)/(1)=mu` `implies" "x=2lambda+1,y=3lambda-1` `z=4lambda+1` and`" "x=mu+3,y=2mu+k,z=mu` are same. `implies" "2lambda+1=mu+3` `3lambda-1=2mu+k` `4lambda+1=mu` On solving Ist and IIIrd terms, we get, `lambda=-(3)/(2)" and "mu=-5` `:." "k=3lambda-2mu-1` `implies" "k=3(-(3)/(2))-2(-5)-1=(9)/(2)` `:." "k=(9)/(2)`

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if the lines `(x-1)/2=(y-1)/3=(z-1)/4 and (x-3)/2=(y-k)/1=z/1` intersect then the value of `k` is (a) `1/3` (b) `2/3` (c) `-1/3` (d) `1`A. `(3)/(2)`B. `(9)/(2)`C. `-(2)/(9)`D. `-(3)/(2)`

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