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The angle between the planes given by combined equation 

6x2 + 4y2 - 10z2 + 3yz + 4zx - 11xy = 0 is equal to

This question was previously asked in
RPSC 2nd Grade Mathematics (Held on 30th June 2017) Official Paper
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  1. cos-1(2/3)
  2. π/2
  3. π/3
  4. cos-1(1/6)

Answer (Detailed Solution Below)

Option 2 : π/2
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Detailed Solution

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Concept Used:

For the equation \(a x^2+b y^2+c z^2+2 f y z+2 g z x+2 h x y=0\) to be a plane equation:
\( \operatorname{det}\left(\begin{array}{lll} a & h & g \\ h & b & f \\ g & f & c \end{array}\right)=0 \)
Then angle between the plane will be given by:-
\( \tan ^{-1}\left[\frac{2 \sqrt{f^2+g^2+h^2-a b-b c-c a}}{a+b+c}\right] \)

Calculation:

given equation: 6x2 + 4y2 - 10z2 + 3yz + 4zx - 11xy = 0

a = 6, b = 4, c = -10, f = 3 / 2, y = 2, h = \(-\frac{11}{2}\)
Angle between both planes is:
\( \begin{aligned} &\Rightarrow \tan ^{-1}\left[\frac{2 \sqrt{9 / 4+4+121 / 4-24+40+60}}{6+4-10}\right] \\ &\Rightarrow \tan ^{-1}\left[\frac{2 \sqrt{9 / 4+4+121 / 4-24+40+60}}{0}\right]=\frac{π}{2} \end{aligned}\)
[tan is not defined at π/2]
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More Equation of a Plane Questions

Q1.The equation of the plane passing through the point (1, 2, –3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z = 7, is:
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