Question

The coordinates of a point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4\sqrt{14}$ from the point $(1,-1,0)$ are

• A. $(9,-13,4)$
• B. $(8\sqrt{14}+1,-12\sqrt{14}-1,4\sqrt{14})$
• C. $(-7,11,-4)$
• D. $(-8\sqrt{14}+1,-12\sqrt{14}-1,-4\sqrt{14})$

Answer 1

Answer: (A), (C)

The correct options are
A $(9,-13,4)$
C $(-7,11,-4)$

Let any point on line $\frac{x-1}{2}=\frac{y+1}{-3}=z=\lambda \left(say\right)$
be $(1+2\lambda ,-1-3\lambda ,\lambda )$
Now using given condition,
$4\sqrt{14}=\sqrt{(1+2\lambda -1{)}^2+(-1-3\lambda +1{)}^2+{\lambda }^2}$
$4\sqrt{14}=\sqrt{4{\lambda }^2+9{\lambda }^2+{\lambda }^2}$
$\Rightarrow |\lambda |=4\Rightarrow \lambda =\pm 4$
$\therefore$ Points $(9,-13,4)$ and $(-7,11,-4)$