First slide

Introduction to 3-D Geometry

Question

$The distance between the origin and the centroid of the tetrahedron whose vertices are (0,0,0), (a,0,0), (0,b,0), (0,0,c) is$

Moderate

A

$\sqrt{a^{2} + b^{2} + c^{2}}$
B

$\frac{\sqrt{a^{2} + b^{2} + c^{2}}}{2}$
C

$\frac{\sqrt{a^{2} + b^{2} + c^{2}}}{4}$
D

$4 \sqrt{a^{2} + b^{2} + c^{2}}$

Solution

Centroid of the tetrahedron $G = (\frac{a}{4}, \frac{b}{4}, \frac{c}{4}) .$
$∴ O G = \frac{\sqrt{a^{2} + b^{2} + c^{2}}}{4}$

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