Find the equation of the bisector planes of the angles between the planes $2 x - y + 2 z + 3 = 0$ and $3 x - 2 y + 6 z + 8 = 0$ .

5 x - y - 4 z - 22 = 0

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23 x - 13 y + 32 z + 26 = 0

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19 x - y - 4 z + 26 = 0

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none of these

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Solution

The correct options are
A $5 x - y - 4 z - 22 = 0$
B $23 x - 13 y + 32 z + 26 = 0$
Equation of the planes is $2 x - 4 y + 2 z + 3 = 0$ and $3 x - 2 y + 6 z + 8 = 0$
Then equation of the plane bisection the angles between them are
$\frac{2 x - 4 y + 2 z + 3}{\sqrt{4 + 16 + 4 + 9}} = \pm \frac{3 x - 2 y + 6 z + 8}{\sqrt{9 + 4 + 36 + 64}}$
$\Rightarrow \frac{2 x - 4 y + 2 z + 3}{\sqrt{33}} = \pm \frac{3 x - 2 y + 6 z + 8}{\sqrt{113}}$
$\Rightarrow 5 x - y - 4 z - 22 = 0$ and $23 x - 13 y + 32 z + 26 = 0$

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Similar questions

2 x - y + 2 z + 3 = 0

3 x - 2 y + 6 z + 8 = 0

2 x - y + 2 z + 3 = 0

3 x - 2 y + 6 z + 8 = 0

2 x - y + 2 z + 3 = 0

3 x - 2 y + 6 z + 8 = 0

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