First slide

Introduction to 3-D Geometry

Question

If feet of perpendiculars from point P( 1 , 2, 3) on xy, yz and zx-plane are A, B and C respectively, then
distance of centroid of tringle ABC from origin is

Moderate

A

$\frac{\sqrt{14}}{3}$
B

$\frac{2 \sqrt{14}}{3}$
C

$\frac{3 \sqrt{14}}{3}$
D

$3 \sqrt{14}$

Solution

Clearly A $\equiv$ (1,2,0), B $\equiv$ (0, 2,3) and C $\equiv$ (1,0,3).
.'. Centroid of triangle ABC is
$\begin{array}{l} G \equiv (\frac{1 + 0 + 1}{3}, \frac{2 + 2 + 0}{3}, \frac{0 + 3 + 3}{3}) \\ \equiv (\frac{2}{3}, \frac{4}{3}, 2) \\ OG = \sqrt{{(\frac{2}{3})}^{2} + {(\frac{4}{3})}^{2} + (2)^{2}} = \frac{2 \sqrt{14}}{3} \end{array}$

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