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NCERT Class XII Mathematics Chapter - - Solutions

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Question : 81 of 78
Marks: +1, -0
Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is
Solution:  
The given planes are
2x + 3y + 4z = 4 ...(1)
and 4x + 6y + 8z = 12 ...(2)
Dividing (2) by 2,
2x + 3y + 4z = 6 ...(3)
Distance between parallel planes (1) and (3)
∣d1−d2a2+b2+c2∣\left|\frac{d_1-d_2}{\sqrt{a^2+b^2+c^2}}\right|
∣4−64+9+16∣=229\left|\frac{4-6}{\sqrt{4+9+16}}\right|=\frac{2}{\sqrt{29}}units
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