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 R_{1}

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

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