Test Index

UPSC NDA Math Model Paper 5

Question : 22 of 120

Marks: +1, -0

2x - y + 3z + 4 = 0

6x - 3y + 9z - 3 = 0?

Solution:

Given: Equation of planes is:

2x - y + 3z + 4 = 0

and

6x - 3y + 9z - 3 = 0

The given equations can be re-written as:

2x - y + 3z + 4 = 0

and

2x - y + 3z - 1 = 0

As we can see that, both the planes are parallel to each other and the distance between two parallel planes is given by:

\left|\frac{d_1 - d_2}{\sqrt{a^2 + b^2 + c^2}}\right|

Here,

a=2, b=-1, c=3, d_1=4

and

d_2 = -1

\Rightarrow \left|\frac{4+1}{\sqrt{2^2 + (-1)^2 + 3^2}}\right|

= \frac{5}{\sqrt{14}}

Go to Question:

Prev Question

Next Question