Question

The planes $2x-y+4z=5$ and $5x-2.5y+10z=6$ are

• A. Perpendicular
• B. Intersect y-axis
• C. Parallel
• D. Passes through $(0,0,\frac{5}{4})$
  

Answer 1

The correct option is C Parallel

Given : Equation of the planes are:
$2x-y+4z=5$ ....(1)
and $5x-2.5y+10z=6$

Simplifying the second equation of the plane

$\Rightarrow \frac{5}{2.5}x-y+\frac{10}{2.5}z=\frac{6}{2.5}$

$\Rightarrow 2x-y+4z=2.4$ ....(2)

Comparing (1) and (2) with

$A_{1}x+B_{1}y+C_{1}z=D_1$ and $A_{2}x+B_{2}y+C_{2}z=D_2$

$\therefore$ Direction ratios of normal to plane (1) are :

$A_1=2,B_1=-1,C_1=4$

And, Direction ratios of normal to plane (2) are :

$A_2=2,B_2=-1,C_2=4$

As the direction ratios of normal for both the planes are same, so they are parallel planes.

Hence, option (B) is correct.