Q. 12

# Prove that the li

Given: The equations of the two lines are and To Prove: The two lines intersect and to find their point of intersection.

Formula Used: Equation of a line is

Vector form: Cartesian form: where is a point on the line and b1 : b2 : b3 is the direction ratios of the line.

Proof:

Let  So a point on the first line is (λ1 + 4, 4λ1 – 3, 7λ1 – 1)

A point on the second line is (2λ2 + 1, -3λ2 – 1, 8λ2 – 10)

If they intersect they should have a common point.

λ1 + 4 = 2λ2 + 1 λ1 – 2λ2 = -3 … (1)

1 – 3 = -3λ2 – 1 1 + 3λ2 = 2 … (2)

Solving (1) and (2),

11λ2 = 14 Therefore, Substituting for the z coordinate, we get and So, the lines do not intersect.

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