What is the distance between $(3, –1, 1)$ and $(–1, 4, –2)$ ?

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Answer 1 · 2018-03-25T20:06:55

$5sqrt(2)$

We are given two points in $RR^3$ .

Let's find a vector that connects these two points, then compute the length of that vector.

$[3,-1,1]-[-1,4,-2]$

$=[(3-(-1), (-1)-4, 1-(-2)]$

$=[4, -5, 3]$

Now the length of this vector is:

$sqrt(4^2+(-5)^2+3^2) = sqrt(16+25+9)$

$=sqrt(50)=sqrt(25*2)=sqrt(25)sqrt(2)=5sqrt(2)$

What is the distance between (3, –1, 1) (3, –1, 1) and (–1, 4, –2) (–1, 4, –2) ?