Question

The equation of the plane which passes through the points $(2,3,-4)$ and $(1,-1,3)$ and is parallel to the $x$-axis is

• A. $7y-4z-5=0$
• B. $4y+7z+5=0$
• C. $4y-7z-5=0$
• D. $7y+4z-5=0$

Answer 1

The correct option is D $7y+4z-5=0$

Equation of the plane parallel to the $x$-axis is $by+cz+d=0$

Since the plane passes through $(2,3,-4),(1,-1,3)$

Thus $3b+4c+d=0$ .... $\left(i\right)$ and $-b+3c+d=0$ .... $\left(ii\right)$

Subtracting $\left(i\right)$ and $\left(ii\right)$ we get

$-4b=-7c⟹\frac{b}{-7}=\frac{c}{-4}=\lambda$

Adding $\left(i\right)$ and $\left(ii\right)$ we get

$5c=-4d⟹\frac{c}{-4}=\frac{d}{5}=\lambda$

$\Rightarrow \frac{b}{-7}=\frac{c}{-4}=\frac{d}{5}=\lambda$

Thus equation of the plane is $7y+4z-5=0$.