Question

Given the points $A(6,-7,0),B(16,-19,-4),C(0,3,-6)$ and $D(2,-5,10)$,the point of intersection of the lines $AB$ and $CD$ is

• A. $(-1,1,2)$
• B. $(1,-1,2)$
• C. $(1,-1,-2)$
• D. $(-1,1,-2)$
• E. $(1,1,2)$

Answer 1

Answer: (B)

$(1,-1,2)$

Answer 2

Given that

$A(6,-7,0),B(16,-19,-4),C(0,3,-6)$ and $D(2,-5,10)$ are the point of intersection of the lines $AB$ and $CD$
So, the point f intersection can be found as ,
Any point on $AB$ can be written as $(6+5x,−7−6x,−2x)$
Any point on $CD$ can be written as $(y,3−4y,−6+8y)$
To find the intersection of $AB$ and $CD$ , the coordinates of the point written in the two different ways should be equal.
Hence,
$6+5x=y$
$−7−6x=3−4y$
$−2x=−6+8y$
The three equations are consistent and on solving we get: $x=−1$ and $y=1$.
Hence, desired point of intersection is $(1,−1,2)$.
So, the correct option is (B) : $(1,−1,2)$