Math 22 The Three-Dimensional Coordinate System

The Three-Dimensional Coordinate System

The Distance and Midpoint Formulas

 The distance $d$ between the points $(x_{1},x_{2},x_{3})$ and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (x_{2},y_{2},z_{2})}
 is
 
 $d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}}$

Exercises 1 Find the distance between two points

1) Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (4,2,3)} and $(1,2,0)$

Solution:
Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}}={\sqrt {(1-4)^{2}+(2-2)^{2}+(0-3)^{2}}}={\sqrt {18}}}

2) Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (1,2,4)} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2,5,1)}

Solution:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d=\sqrt{(2-1)^2+(5-2)^2+(1-4)^2}=\sqrt{19}}

Midpoint Formula in Space

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