Q23 of 26 Page 1

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

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


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