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What is the pythagoras-based formula for the distance between two points for a 3D vector?

3 years ago

ยท

2 Replies

ยท

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M

Madeline Mcglynn


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2 Answers

Alex C Profile Picture
Alex C Verified Sherpa Tutor โœ“

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It follows a very similar format to the pythagoras formula in 2D, in 3D it is: sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

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Simon Profile Picture
Simon Verified Sherpa Tutor โœ“

Sussex University graduate who just can't get enough of maths!

Hi Madeline!


If your two points are (xโ‚, yโ‚, zโ‚) and (xโ‚‚, yโ‚‚, zโ‚‚), then the formula is:

Distance = โˆš[(xโ‚โ€“xโ‚‚)ยฒ + (yโ‚โ€“yโ‚‚)ยฒ + (zโ‚โ€“zโ‚‚)ยฒ]


For example, let's say you want to find the distance between the points (โ€“6, 4, โ€“15) and (2, โ€“5, โ€“3):

Distance = โˆš[(โ€“6โ€“2)ยฒ + (4โ€“(โ€“5))ยฒ + (โ€“15โ€“(โ€“3))ยฒ]

= โˆš[(โ€“8)ยฒ + (9)ยฒ + (โ€“12)ยฒ]

= โˆš[64 + 81 + 144]

= โˆš[289]

= 17


Simon


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