Practicing Success
By using equations of the line $\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}$ and the plane $10 x+2 y-11 z-3=0$, answer the following questions. |
The foot of perpendicular from the origin to the given plane is |
$\left(\frac{2}{75}, \frac{2}{15},-\frac{11}{75}\right)$ $\left(\frac{2}{15}, \frac{2}{75},-\frac{11}{75}\right)$ $\left(\frac{2}{5}, \frac{2}{25}, \frac{11}{25}\right)$ $\left(\frac{2}{5}, \frac{2}{25},-\frac{11}{25}\right)$ |
$\left(\frac{2}{15}, \frac{2}{75},-\frac{11}{75}\right)$ |
Let foot of perpendicular = (p, q, r) so from (0, 0, 0) so $\frac{p-0}{10}=\frac{q-0}{2}=\frac{r-0}{-11}=\frac{-(-3)}{\left(10^2+2^2+(-11)^2\right)}$ $\Rightarrow \frac{p}{10}=\frac{q}{2}=\frac{r}{-11}=\frac{3}{225} \Rightarrow (p, q, r)$ $=\left(\frac{30}{225}, \frac{6}{225}, \frac{-33}{225}\right)$ $=\left(\frac{2}{15}, \frac{2}{75}, \frac{-11}{75}\right)$ Option: B |