JEE MATHEMATICS MCQ: 3D PLANES

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Application +4 | -1

A variable plane is at a constant distance '

r

' from the origin and meets the axes in

A, B, C

then, the locus of the centroid of the tetrahedron

{OABC}

is-

View answer and explanation

Correct option: A

\frac{1}{{x}^2}+\frac{1}{{y}^2}+\frac{1}{{z}^2}=\frac{16}{{r}^2}

Option A (

\frac{1}{{x}^2}+\frac{1}{{y}^2}+\frac{1}{{z}^2}=\frac{16}{{r}^2}

) is correct because it represents the locus of the centroid of the tetrahedron, derived from the equation of the plane and the centroid coordinates.

More Questions from 3D PLANES

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\alpha

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\mathrm{ax}+\mathrm{by} \pm \mathrm{z} \sqrt{\mathrm{a}^2+\mathrm{b}^2} \tan \alpha+\mathrm{c}=0

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x, y

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A, B

C

y z

A

z x

B

x y

C