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Question

Mathematics Question on Three Dimensional Geometry

What is the length of the perpendicular from the origin to the plane ax+by+2abz=1ax + by + \sqrt{2ab} z = 1 ?

A

1/(ab)

B

1/(a + b)

C

a + b

D

ab

Answer

1/(a + b)

Explanation

Solution

Length of perpendicular from the origin to the plane ax+by+2abz−1=0ax + by + \sqrt{2ab } z -1 = 0 is =∣0+0+0−1a2+b2+2ab∣=1(a+b)2=1(a+b)= \left| \frac{0+0+0-1}{\sqrt{a^{2} + b^{2}+2ab}}\right| = \frac{1}{\sqrt{\left(a +b\right)^{2}}} = \frac{1}{\left(a +b\right)}