First slide

Introduction to 3-D Geometry

Question

If feet of perpendiculars from point P(1,2,3) on x,y and z-axis are A,B and C respectively ,then distance of centroid of triangle ABC from origin is

Moderate

A

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

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

$\sqrt{14}$
D

$3 \sqrt{14}$

Solution

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

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