Find the angle between planes 2x +7y +11z - 3 = 0 & 5x +3y +9z +1 = 0

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Solution

The correct option is A
We know that the angle between two planes $a_{1} x + b_{1} y + c_{1} z + d_{1} = 0$ & $a_{2} x + b_{2} y + c_{2} z + d_{2} = 0$ is given by -
$c o s (θ) = \frac{a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2}}{\sqrt{(a_{1}^{2} + b_{1}^{2} + c_{1}^{2}) (a_{2}^{2} + b_{2}^{2} + c_{2}^{2})}}$
So, Here we’ll substitute the appropriate values.
$c o s (θ) = \frac{2.5 + 7.3 + 11.9}{\sqrt{(2^{2} + 7^{2} + 11^{2}) (5^{2} + 3^{2} + 9^{2})}}$
$c o s (θ) = \frac{130}{\sqrt{174} . \sqrt{115}}$
$(θ) = c o s^{- 1} (\frac{127}{\sqrt{174} \sqrt{115}})$

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Similar questions

Find the angle between the planes
$2 x + 7 y + 11 z - 3 = 0 and 5 x + 3 y + 9 z + 1 = 0$

2 x + 7 y + 11 z - 3 = 0

5 x + 3 y + 9 z + 1 = 0

2 x + 2 y - 3 z - 5 = 0

3 x - 3 y + 5 z - 3 = 0

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