The plane 2x-(1- )y+3 =0 passes through the intersection of the p… - Vidyadip

MCQ

The plane $2\text{x}-(1-\lambda)\text{y}+3\lambda\text{z}=0$ passes through the intersection of the planes:

✓
$2x - y = 0$ and $y- 3z = 0$
B
$2x + 3z = 0$ and $y = 0$
C
$2x - y + 3z = 0$ and $y - 3z = 0$
D
None of these

✓

Answer

Correct option: A.

$2x - y = 0$ and $y- 3z = 0$

The given plane is
$2\text{x}-(1-\lambda)\text{y}+3\lambda\text{z}=0$
$\Rightarrow(2\text{x}-\text{y})+\lambda(-\text{y}+3\text{z})=0$
So, this plane passes through the intersection of the planes
$2x - y = 0$ and $-y + 3z = 0$
$\Rightarrow 2x - y = 0$ and $y - 3z = 0.$

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