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What is the distance between #(3, –1, 1) # and #(6, 0, 4) #?

Answer 1

Hazel Anglin

The distance between (3, –1, 1) and (6, 0, 4) is √26.

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Answer 2

Eli Assouline

See a solution process below:

The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(6) - color(blue)(3))^2 + (color(red)(0) - color(blue)(-1))^2 + (color(red)(4) - color(blue)(1))^2)#

#d = sqrt((color(red)(6) - color(blue)(3))^2 + (color(red)(0) + color(blue)(1))^2 + (color(red)(4) - color(blue)(1))^2)#

#d = sqrt(3^2 + 1^2 + 3^2)#

#d = sqrt(9 + 1 + 9)#

#d = sqrt(19)#

#d = 4.359# rounded to the nearest thousandth.

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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.