Equation of a plane passing through (1,1,1) and containing X-axis… - Vidyadip

MCQ

Equation of a plane passing through $(1,1,1)$ and containing $X$-axis is

A
$x-y=0$
B
$x- z =0$
✓
$y- z =0$
D
$x+y+ z =3$

✓

Answer

Correct option: C.

$y- z =0$

(C)
Since, the plane contains the X -axis, it passes through the origin
$\therefore \quad d =0$
$\therefore \quad$ The equation of the plane is
$a x+b y+c z=0...(i)$
Also, plane passes through $(1,1,1)$
$\therefore \quad a+b+c=0...(ii)$
The equation of the X-axis is $\frac{x}{1}=\frac{y}{0}=\frac{z}{0}$
As the plane contains the X -axis, the d.r.s of the normal to the plane are perpendicular to X-axis
$\therefore \quad a(1)+b(0)+c(0)=0$
$\Rightarrow a =0$
Substituting value of $a$ in (ii) we get
$b+c=0 \Rightarrow b=-c$
$\therefore \quad$ The equation of the required plane is $b y- bz =0$
$\Rightarrow y-z=0$

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