# Distance between (3,-1,1) and (-1,4,-2)?

seguitzi2 2022-10-09 Answered
Distance between (3,-1,1) and (-1,4,-2)?
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## Answers (1)

Jane Reese
Answered 2022-10-10 Author has 8 answers
We are given two points in ${ℝ}^{3}$.
Let's find a vector that connects these two points, then compute the length of that vector.
$\left[3,-1,1\right]-\left[-1,4,-2\right]$
$=\left[\left(3-\left(-1\right),\left(-1\right)-4,1-\left(-2\right)\right]$
$=\left[4,-5,3\right]$
Now the length of this vector is:
$\sqrt{{4}^{2}+{\left(-5\right)}^{2}+{3}^{2}}=\sqrt{16+25+9}$
$=\sqrt{50}=\sqrt{25\cdot 2}=\sqrt{25}\sqrt{2}=5\sqrt{2}$
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