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Three Dimensional Geometry

Question
CBSEENMA12033368
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Find the angle between the planes
2x – y + z = 6 and x + y + 2z = 7

Solution

The equation of two planes are
2 x – y + z = 6
and x + y + 2 z = 7
Let θ be the angle between the planes
therefore space space space space space space cos space straight theta space equals space fraction numerator left parenthesis 2 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis negative 1 right parenthesis thin space left parenthesis 1 right parenthesis space plus space left parenthesis 1 right parenthesis thin space left parenthesis 2 right parenthesis over denominator square root of 4 plus 1 plus 1 end root space square root of 1 plus 1 plus 4 end root end fraction space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 2 minus 1 plus 2 over denominator square root of 6 space square root of 6 end fraction space equals space 3 over 6 space equals space 1 half therefore space space space space space space space straight theta space space equals space straight pi over 3

Some More Questions From Three Dimensional Geometry Chapter

If α, β, γ are the angles which a line makes with the axes, prove that sin2α + sin2 β + sin2γ = 2.

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