Question

If the line joining $A(1,3,4)$ and $B$ is divided by the point $(-2,3,5)$ in the ratio $1:3$, then $B$ is

• A. (-11,3,8)
• B. (-11,3,-8)
• C. (-8,12,20)
• D. (13,6,-13)

Answer 1

Answer: (A)

Using internally ratio formula, $(-2,3,5)$
$=\left(\frac{1\times x+3\times 1}{1+3},\frac{1\times y+3\times 3}{1+3},\frac{1\times z+3\times 4}{1+3}\right)$
$\Rightarrow (2,3,5)=\left(\frac{x+3}{4},\frac{y+9}{4},\frac{z+12}{4}\right)$
$\Rightarrow x+3=-8,y+9=12,z=12=20$
$\Rightarrow x=-11,y=+3,z=8$
$\therefore$ Required point $=B(-11,3,8)$