Question

Given $A(1,-1,0)$; $B(3,1,2)$;$C(2,-2,4)$ and $D(-1,1,-1)$ which of the following points neither lie on $AB$ nor on $CD$

• A. $(2,2,4)$
• B. $(2,-2,4)$
• C. $(2,0,1)$
• D. $(0,-2,-1)$

Answer 1

The correct option is A $(2,2,4)$

Given:- $A(1,-1,0)$; $B(3,1,2)$;$C(2,-2,4)$ and $D(-1,1,-1)$

The equation of line $AB$ is given by $r=i-j+t(2i+2j+2k)$ or $\frac{x-1}{2}=\frac{y+1}{2}=\frac{z}{2}$

The points $(2,0,1)$ and $(0,-2,1)$ lies on $AB$.

The equation of line $CD$ is given by $r=2i-2j+4k+t(3i-3j+5k)$ or $\frac{x-2}{3}=\frac{y+2}{-3}=\frac{z-4}{5}$

$(2,-2,4)$ lie on $CD$.

$(2,2,4)$ does not lie on any of the lines AB or CD.

Hence, option A is correct.