Q. 185.0( 1 Vote )

Show that the lines and intersect. Find their point of intersection.

Answer :

Given:

and


Now, let



x – 1 = 3λ, y – 1 = -λ and z + 1 = 0


x = 3λ + 1, y = -λ + 1 and z = -1


Let



x – 4 = 2μ, y = 0 and z + 1 = 3μ


x = 2μ + 4, y = 0 and z = 3μ – 1


If lines intersect, then they have a common point for some value of λ and μ


So, 3λ + 1 = 2μ + 4 [comparing the values of x]


3λ – 2μ = 4 – 1


3λ – 2μ = 3 …(i)


and –λ + 1 = 0 [comparing the values of y]


λ = 1


and -1 = 3μ – 1


-1 + 1 = 3μ


μ = 0


Now, putting the values of λ and μ in eq. (i), we get


3(1) – 2(0) = 3


3 = 3


Since, λ = 1 and μ = 0 satisfy equation (i) so the given lines intersect.


Now, the point of intersection are


x = 3λ + 1, y = -λ + 1 and z = -1


x = 3(1) + 1, y = -(1) + 1 and z = -1


x = 4 , y = 0 and z = -1


Point of intersection are (4, 0, -1)


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