First slide

Introduction to 3-D Geometry

Question

If $x^{2} + y^{2} = 1$ then the distance from the point $(x, y, \sqrt{1 - x^{2} - y^{2}})$ to the origin is

Easy

A

1
B

-1
C

0
D

2

Solution

Distance from point $(x, y, \sqrt{1 - x^{2} - y^{2}})$ to the origin
$\begin{array}{l} = \sqrt{{(x - 0)^{2} + (y - 0)^{2} + \sqrt{(1 - x^{2} - y^{2}} - 0)}^{2}} \\ = \sqrt{x^{2} + y^{2} + 1 - x^{2} - y^{2}} \\ = \sqrt{1 + 1 - (1)} [∵ x^{2} + y^{2} = 1 given] \\ = \sqrt{1} = 1 \end{array}$

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