Question

The coordinates of the foot of the perpendicular drawn form the origin to the plane $2x+3y+4z-12=0$ is

• A. $(\frac{36}{29},\frac{24}{29},\frac{48}{29})$
• B. $(\frac{24}{29},\frac{48}{29},\frac{36}{29})$
• C. $(\frac{24}{29},\frac{36}{29},\frac{48}{29})$
• D. None of these

Answer 1

The correct option is C $(\frac{24}{29},\frac{36}{29},\frac{48}{29})$

The line has DR's $(2,3,4)$ and it passes through origin

line is $\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=k$

any point on line is $(2k,3k,4k)$ putting this point on plane

$2\left(2k\right)+3\left(3k\right)+4\left(4k\right)-12=0$

$29k=12$

$k=\frac{12}{29}$

point is $(2\left(\frac{12}{29}\right),3\left(\frac{12}{29}\right),4\left(\frac{12}{29}\right))\equiv (\frac{24}{29},\frac{36}{29},\frac{48}{29})$