Respuesta :

smmwaite
The general formula for getting the distance between two points is. √(x²+y²+z²).
 
So the distance of A from the origin is;
 √(5²+3²+4²) = √(25+3+16)
                     =√50
                     =7.1

The distance of B from the origin;
 √((-4)²+2²+6²) = √(16+4+36)
                       = √80.28427125
                       =9.0
 
danielmaduroh
Given the two points [tex]P_{1}(x_{1}, y_{1} , z_{1})[/tex] and [tex]P_{2}(x_{2}, y_{2} , z_{2})[/tex] the distance d between these points is given by the formula:

[tex]d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}[/tex]

Given that the problem ask for the distance A from the origin and B from the origin, we're going to calculate two distances:

Distance 1:

[tex]P_{1} = P_{1}(0,0,0)[/tex]
[tex]P_{2}=A(5, 3, 4)[/tex]

So:
[tex]d_{1} = \sqrt{(5-0)^{2}+(3-0)^{2}+(4-0)^{2}}[/tex]
[tex]d_{1} = 7.07[/tex]

Distance 2:

[tex]P_{1} = P_{1}(0,0,0)[/tex]
[tex]P_{2}=A(-4,2,6)[/tex]

So:
[tex]d_{2} = \sqrt{(-4-0)^{2}+(2-0)^{2}+(6-0)^{2}}[/tex]
[tex]d_{2} = 7.48[/tex]


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