First slide

Introduction to 3-D Geometry

Question

Distance of the point (1,2,3) from the coordinate axes are

Easy

A

13, 10, 5
B

$\sqrt{13}, \sqrt{10}, \sqrt{5}$
C

$\sqrt{5}, \sqrt{13}, \sqrt{10}$
D

$\frac{1}{\sqrt{13}}, \frac{1}{\sqrt{10}}, \frac{1}{\sqrt{5}}$

Solution

Let point be P(x,y, z) = (1 ,2,3)
The distance from r-axis $= \sqrt{y^{2} + z^{2}}$
$= \sqrt{4 + 9} = \sqrt{13}$
The distance from y-axis $= \sqrt{x^{2} + z^{2}} = \sqrt{1^{2} + 3^{2}}$
$= \sqrt{1 + 9} = \sqrt{10}$
The distance from z-axis $= \sqrt{x^{2} + y^{2}} = \sqrt{1^{2} + 2^{2}}$
$= \sqrt{1 + 4} = \sqrt{5}$

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