Question

If a plane passes through intersection of planes $\text{2x-y-4 = 0}$ and $\text{y+2z-4 = 0}$ and also passes through the point$\text{(1, 1, 0)}$. Then the equation of the plane is

• A. $\text{x-y-z = 0}$
• B. $\text{2x-z = 0}$
• C. $\text{x+2z-1 = 0}$
• D. $\text{x-z-1 = 0}$

Answer 1

The correct option is A

$\text{x-y-z = 0}$

Explanation for the correct option :

Step 1. Given data

Given planes are $\text{2x-y-4 = 0}$ and $\text{y+2z-4 = 0}$

Therefore, the equation of the required plane is $\text{(2x-y-4)+λ(y+2z-4) = 0}$ $\dots \dots \left(1\right)$

Step 2. Equation of the plane

Given that, the plane passes through the point $\text{(1,1,0)}$

By substituting in equation $\left(1\right)$, we get $\text{(2-1-4)+λ(1+0-4) = 0}$

$\Rightarrow \lambda =-1$

Step 3. Substitute $\mathit{\lambda }\mathbf{}$value

By substituting $\lambda =-1$ in equation $\left(1\right)$, we get

(2x-y-4)-(y+2z-4) = 0

2x-2y-2z = 0

x-y-z = 0

Hence, option $\mathbf{\text{"A"}}$ is correct.