Given: The equations of the two lines are
To Prove: The two lines intersect and to find their point of intersection.
Formula Used: Equation of a line is
where is a point on the line and b1 : b2 : b3 is the direction ratios of the line.
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)
4λ1 – 3 = -3λ2 – 1 ⇒ 4λ1 + 3λ2 = 2 … (2)
Solving (1) and (2),
11λ2 = 14
Substituting for the z coordinate, we get
So, the lines do not intersect.
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