Question

Given points A(1,2,3), B(−3,2, −4), C(−2,1,5), find the following magnitudes.
a. ||AB||

Answer 1

`||AB||=√(65)`

Explanation:

If you have two points:

`A=(x_1,y_1,z_1)\\B=(x_2,y_2,z_2)\\\\||AB||=√((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`

Then, we have:

`A=(1,2,3)\\B=(-3,2,-4)`

And we have to calculate
`||AB||`

`||AB||=√((-3-1)^2+(2-2)^2+(-4-3)^2)\\\\||AB||=√((-4)^2+(0)^2+(-7)^2)\\\\||AB||=√(16+49) \\\\||AB||=√(65)`

The answer is:

`||AB||=√(65)`