# Algebra Examples

,

Step 1

To find the distance between two 3d points, square the difference of the x, y, and z points. Then, sum them and take the square root.

Step 2

Replace , , , , , and with the corresponding values.

Step 3

Step 3.1

Simplify each term.

Step 3.1.1

Multiply by each element of the matrix.

Step 3.1.2

Multiply by .

Step 3.2

Simplify the expression.

Step 3.2.1

Add and .

Step 3.2.2

Raising to any positive power yields .

Step 3.3

Simplify each term.

Step 3.3.1

Multiply by each element of the matrix.

Step 3.3.2

Multiply by .

Step 3.4

Simplify the expression.

Step 3.4.1

Add and .

Step 3.4.2

Raise to the power of .

Step 3.4.3

Subtract from .

Step 3.4.4

Raise to the power of .

Step 3.4.5

Add and .

Step 3.4.6

Add and .

Step 4

The distance between and is .