Calculating Distance in 3 Dimensions: Mastering the Distance Formula in Math

Distance Formula in 3 Dimensions

The distance formula in 3 dimensions is an extension of the distance formula we use in 2 dimensions

The distance formula in 3 dimensions is an extension of the distance formula we use in 2 dimensions. In 2 dimensions, the distance between two points (x1,y1) and (x2,y2) can be calculated using the formula:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

In 3 dimensions, the distance between two points (x1,y1,z1) and (x2,y2,z2) can be calculated using a similar formula:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2)

Let’s break down the steps to find the distance between two points in 3 dimensions:

Step 1: Identify the coordinates of the two points.
Let’s say we have point A with coordinates (x1, y1, z1) and point B with coordinates (x2, y2, z2).

Step 2: Calculate the differences of the respective coordinates.
Find the differences between the corresponding coordinates of the two points:
Δx = x2 – x1
Δy = y2 – y1
Δz = z2 – z1

Step 3: Square the differences.
Square each of the differences calculated in step 2:
(Δx)^2, (Δy)^2, and (Δz)^2

Step 4: Add the squared differences.
Add the squared differences calculated in step 3:
(Δx)^2 + (Δy)^2 + (Δz)^2

Step 5: Take the square root.
Take the square root of the sum calculated in step 4:
d = sqrt((Δx)^2 + (Δy)^2 + (Δz)^2)

This will give you the distance between the two given points in 3 dimensions.

It’s important to note that this formula works in any number of dimensions. In 3 dimensions, we consider the x, y, and z coordinates, and in higher dimensions, we would consider additional variables.

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