Question

The equation of the passing through the points (2, -1, 0), (3 ,-4, 5) and parallel to the line $2x=3y=4z$ is

• A. $125x-90y-79z=340$
• B. $32x-21y-36z=85$
• C. $73x+61y-22z=85$
• D. $29x-27y-22z=85$

Answer 1

The correct option is D $29x-27y-22z=85$

we get

$\frac{x}{\frac{1}{2}}=\frac{y}{\frac{1}{3}}=\frac{z}{\frac{1}{4}}$

$a\left(x-2\right)+b\left(y+1\right)+cz=0$

$\frac{a}{2}+\frac{b}{3}+\frac{c}{4}=0$ $\left[planeisparalleltoline\right]$

$6a+4b+3c=0$

$a-3b+5c=0$ $\left[planepassingthorugh(3,-4,5)\right]$

$\frac{a}{20+9}=\frac{-b}{30-3}=\frac{c}{-18-4}$

$\frac{a}{29}=\frac{b}{-27}=\frac{c}{-22}$

$29x-27y-22z=58+27$

$29x-27y-22z=85$

Hence, the option $D$ is the correct answer.