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Question
If A(6,−7,0), B(16,−19,−4), C(0,3,−6) and D(2,−5,10) are four points in space, then the point of intersection of the lines AB and CD is
If A(6,−7,0), B(16,−19,−4), C(0,3,−6) and D(2,−5,10) are four points in space, then the point of intersection of the lines AB and CD is
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Solution
The correct option is B (1,−1,2)
Any point on AB can be written as (6+5t,−7−6t,−2t)
Any point on CD can be written as (u,3−4u,−6+8u)
To find the intersection of AB and CD (if it exists), the coordinates of the point written in the two different ways should be equal.
Hence,
6+5t=u
−7−6t=3−4u
−2t=−6+8u
The three equations are consistent and on solving we get t=−1 and u=1.
Hence, the point of intersection is (1,−1,2).
Any point on AB can be written as (6+5t,−7−6t,−2t)
Any point on CD can be written as (u,3−4u,−6+8u)
To find the intersection of AB and CD (if it exists), the coordinates of the point written in the two different ways should be equal.
Hence,
6+5t=u
−7−6t=3−4u
−2t=−6+8u
The three equations are consistent and on solving we get t=−1 and u=1.
Hence, the point of intersection is (1,−1,2).
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