Q. 234.5( 2 Votes )

If lines and intersect, then find the value of k and hence find the equation of the plane containing these lines.

Answer :

We have, (i)


And (ii)


Let P (α ,β ,γ ) is an intersecting point of line (i) and (ii)


(α, β ,γ ) satisfies line (i)



α = 2λ +1 , β = 3λ -1 , γ = 4λ +1


Also (α ,β ,γ ) lies on line (ii)




Now,



2λ -2 = 4λ +1


2λ -4λ = 2+1


-2λ = 3



Now,



3λ -1-k = 8λ +2


3λ -8λ = 1+k+2


-5λ-3 = k




Equation of plane containing these lines is



Expanding along R1


(x-1)(3-8) –(y+1)(2-4)+(z-1)(4-3)=0


-5(x-1)+2(y+1)+(z-1)=0


-5x+5+2y+2+z-1=0


-5x+2y+z+6=0


5x-2y-z-6=0


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses