Answer:
[tex]||AB||=\sqrt{65}[/tex]
Step-by-step explanation:
If you have two points:
[tex]A=(x_1,y_1,z_1)\\B=(x_2,y_2,z_2)\\\\||AB||=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]
Then, we have:
[tex]A=(1,2,3)\\B=(-3,2,-4)[/tex]
And we have to calculate [tex]||AB||[/tex]
[tex]||AB||=\sqrt{(-3-1)^2+(2-2)^2+(-4-3)^2}\\\\||AB||=\sqrt{(-4)^2+(0)^2+(-7)^2}\\\\||AB||=\sqrt{16+49} \\\\||AB||=\sqrt{65}[/tex]
The answer is:
[tex]||AB||=\sqrt{65}[/tex]
