The distance of the point (7,10,11) from the line (x-4)/(1)=(y-4)/(0)=(z-2)/(3) along the …

Question

The distance of the point $(7,10,11)$ from the line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

Accepted Answer

Equation of line passing through $P(7,10,11)$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

$$\frac{x-7}{2}=\frac{y-10}{3}=\frac{z-11}{6}=\lambda$$

Let the point on the line is

$$Q(2 \lambda+7,3 \lambda+10,6 \lambda+11)$$

$Q$ lies on line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$

$$\begin{aligned}
& 3 \lambda+10=4 \Rightarrow \lambda=-2 \
& \therefore \quad Q(3,4,-1) \
& P Q=\sqrt{16+36+144}=14
\end{aligned}$$

Solutions · 1