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)


2λ -2 = 4λ +1

2λ -4λ = 2+1

-2λ = 3


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





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