Question

Which of the following point(s) lies on the line joining points $A(-2,1,-1)$ and $B(2,-3,-4)$ ?

• A. $(6,7,-7)$
• B. $(6,-7,-7)$
• C. $(6,-5,2)$
• D. $(-6,5,2)$

Answer 1

Answer: (B), (D)

$(-6,5,2)$

Given points : $A(-2,1,-1)$ and $B(2,-3,-4)$
d.r's of line $AB$ is $(a,b,c)=(2+2,-3-1,-4+1)=(4,-4,-3)$
Equation of line $AB:$
$\frac{x+2}{4}=\frac{y-1}{-4}=\frac{z+1}{-3}$
any point on the line $AB$ can be given as :
$=(-2+4{\lambda }_1,1-4{\lambda }_1,-1-3{\lambda }_1)$
for ${\lambda }_1=2:P_1(6,-7,-7)$
for ${\lambda }_1=-1:P_2(-6,5,2)$