Question

Find the points on the line $\frac{x+2}{3}=\frac{y+1}{2}=\frac{z-3}{2}$ at a distance of $5$ units from the points $(1,3,3)$.

Answer 1

$\to$ General point on the

line would be

$(3\lambda -2,2\lambda -1,2\lambda +3)$

it is at distance 5 units

from $(1,3,3)$

$\to \sqrt{(3\lambda -3{)}^2+(2\lambda -4{)}^2+(2\lambda {)}^2}=5$

$\Rightarrow 17{\lambda }^2+25-34\lambda =25$

$\Rightarrow 17\lambda (\lambda -2)=0$

$\Rightarrow \lambda =0$ or $\lambda =2$

$\Rightarrow$ Posible points :-

$(-2,-1,3),(4,3,7)$