Which of the following planes is equally inclined to the planes $4 x + 3 y - 5 z = 0$ and $5 x - 12 y + 13 z = 0$ ?

11 x - 3 y = 0

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3 x + 11 y = 0

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3 x + 11 y = 65 z

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none of these

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Solution

The correct option is D $11 x - 3 y = 0$
The bisector of planes $4 x + 3 y - 5 z = 0$ & $5 x - 12 y + 13 z = 0$ can be given by
$\frac{4 x + 3 y - 5 z}{\sqrt{4^{2} + 3^{2} + 5^{2}}} \pm \frac{5 x - 12 y + 13 z}{\sqrt{5^{2} + 12^{2} + 13^{2}}} = 0$
$\Rightarrow 52 x + 39 y - 65 z \pm (25 x - 60 y + 65 z) = 0$
$\Rightarrow 11 x - 3 y = 0$ and $27 x + 99 y - 130 z = 0$
Ans: A

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Similar questions

Which of the following plane is equally inclined to the planes 4x + 3y – 5z = 0 and 5x – 12y + 13z = 0 is

3 x + 4 y - 5 z + 1 = 0, 5 x + 12 y - 13 z = 0

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

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

The value of $λ$ for which the lines 3x – 4y – 13 = 0, 8x – 11y – 33 = 0 and 2x – 3y + $λ = 0$ are concurrent is

λ

3 x - 4 y - 13 = 0, 8 x - 11 y - 33 = 0

2 x - 3 y + λ = 0

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