The two planes a x+b y+c z+d=0 and a x+b y+c z+d₁=0, where d ≠ d₁, have

Correct Answer is : no points in common

Correct Answer is : no points in common

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UPSC NDA Math Model Paper 8

Question : 62 of 120

Marks: +1, -0

The two planes

a x+b y+c z+d=0

a x+b y+c z+d_{1}=0

d \neq d_{1}

, have

Solution:

Given, the equation of two planes ax + by + cz + d = 0 and ax + by + cz +

d_1

= 0, where

d \neq d_1

Taking the ratio of direction ratios of the plane, we have

\Rightarrow \frac{a}{a}=\frac{b}{b}=\frac{c}{c}

\Rightarrow 1=1=1

The ratio of direction ratios of the plane

\Rightarrow a x+b y+c z+d=0

and

a x+b y+c z+d_{1}=0

is same

\Rightarrow

The plane

a x+b y+c z+d=0

and

a x+b y+c z+d_{1}=0

are parallel.

Hence, The two planes

a x+b y+c z+d=0

and

a x+b y+c z+d_{1}=0

, where

d \neq d_{1}

, have no points in common.

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