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

Answer 1

Savannah Anderson

The distance between (3, –1, 1) and (–1, 4, –2) is approximately 7.07 units.

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Answer 2

Abigail Allen

#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)#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.