# Section / ratio – 3 dimensions Calculator

Insert the given values and calculate Section/ratio – 3 dimensions by using this calculator internally and externally.

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## Section/ratio – 3 dimensions

A section or cross-section is the shape that results from cutting a three-dimensional object with a plane in mathematics. This cut produces a two-dimensional form that symbolizes the point where the item and the plane intersect.

Ratio Externally

(mx2-nx1/m-n, my2-ny1/m-n, mz2-nz1/m-n)

Ratio Internally

(m(x2) +n(x1)/m+n, m(y2) +n(y1)/m+n, m(z2) +n(z1)/m+n)

## Solved Examples

### Example 1:

Evaluate the coordinates of the point divided by the line joining with two points (1, 2, 3) and (1, 2, 3) by the ratio of 1:2 internally.

Solution

Step 1:

Write the data.

x1 = 1, y1 = 2, z1 = 3 and

x2 = 2, y2 = 1, z2 = 3

m = 1, n = 2

Step 2:

The formula for 3-dimensional section/ratio.

(mx2+nx1/m+n, my2+ny1/m+n, mz2+nz1/m+n)

Step 3:

Use the above formula and simplify.

x1 = 1, y1 = 2, z1 = 3 and x2 = 2, y2 = 1, z2 = 3, m = 1, n = 2

(mx2+nx1/m+n, my2+ny1/m+n, mz2+nz1/m+n)

= (1*2+2*1/1+2, 1*1+2*2/1+2, 1*3+2*3/1+2)

= (2+2/3, 1+4/3, 3+6/3)

= (4/3, 5/3, 9/3)

= (1.3, 1.6, 3)

### Example 2:

Evaluate the coordinates of the point divided by the line joining with two points (1, 3, 5) and (2, 3, 4) by the ratio of 2:3 externally.

Solution

Step 1:

Write the data.

x1 = 1, y1 = 3, z1 = 5 and

x2 = 2, y2 = 3, z2 = 4

m = 2, n = 3

Step 2:

The formula for 3-dimensional section/ratio.

(mx2-nx1/m-n, my2-ny1/m-n, mz2-nz1/m-n)

Step 3:

Use the above formula and simplify.

x1 = 1, y1 = 3, z1 = 5 and x2 = 2, y2 = 3, z2 = 4, m = 2, n = 3

= (mx2-nx1/m-n, my2-ny1/m-n, mz2-nz1/m-n)

= (2*2-3*1/2-3, 2*3-3*3/2-3, 2*4-3*5/2-3)

= (4-3/-1, 6-9/-1, 8-15/-1)

= (1/-1, -3/-1, -7/-1)

= (-1, 3, 7)