Q21 of 45 Page 1

Show that the linesandintersect. Also find their point of intersection.

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 = 3λ -1 , β = 5λ -3 , γ = 7λ -5


Also (α ,β ,γ ) lies on line (ii)





Now,



⇒ 9λ -9 = 5λ -7


⇒ 9λ -5λ = 9 -7


⇒4λ = 2



Also,



⇒ 25λ -35 = 21λ -33


⇒ 4λ = 2



Since, the value of λ is same.


∴ both lines intersect each other at P(α ,β ,γ )


⇒ point of intersection = P(α ,β ,γ )


= (α = 3λ -1, β = 5λ -3 , γ = 7λ -5)




Thus, point of intersection =


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