Question

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

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

Answer 1

The correct option is B

$29x-27y–22z=85$

Let the required plane be $ax+by+cz=1$

Equation of the line is $\frac{x}{6}=\frac{y}{4}=\frac{z}{3}$

$\therefore 6a+4b+3c=0$ ... (1)

The plane passes through $(2,-1,0)\Rightarrow 2a-b=1$ ... (2)

It also passes through $(3,-4,5)\Rightarrow 3a-4b+5c=1$ ... (3)

Solving equations (1), (2) and (3), we get

$\Rightarrow a=\frac{29}{85},b=\frac{-27}{85},c=\frac{-22}{85}$

Hence, the equation of the plane is $29x-27y-22z=85$