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Walchand College of Engineering (WCE), Sangli
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## Distance between plane in normal formal and point Solution

STEP 0: Pre-Calculation Summary
Formula Used
length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1))
L = modulus((a1*X)+(b2*Y)+(c3*Z)-(CoefConstant_plane1))
This formula uses 2 Functions, 7 Variables
Functions Used
mod - Modulo function, mod(dividend, divisor)
modulus - Modulus of number, modulus
Variables Used
Direction Ratio 1 - Direction Ratio 1 is ratio proportional to direction cosine w.r.to x axis. (Measured in Hundred)
X Coordinate in 3D Space - X Coordinate in 3D Space is defined as the a point on x axis. (Measured in Hundred)
Direction Ratio 2- Direction Ratio 2 is ratio proportional to direction cosine w.r.to y axis.
Y Coordinate in 3D Space - Y Coordinate in 3D Space is defined as the a point on y axis. (Measured in Hundred)
Direction Ratio 3 - Direction Ratio 3 is ratio proportional to direction cosine w.r.to z axis. (Measured in Hundred)
Z Coordinate in 3D Space - Z Coordinate in 3D Space is defined as the a point on z axis. (Measured in Hundred)
Constant Coefficient of Plane1 - Constant Coefficient of Plane1 is defined as a number which is constant in plane of form lx + my + nz = p. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
Direction Ratio 1: 0.7 Hundred --> 0.7 Hundred No Conversion Required
X Coordinate in 3D Space: 2 Hundred --> 2 Hundred No Conversion Required
Direction Ratio 2: 0.2 --> No Conversion Required
Y Coordinate in 3D Space: 5 Hundred --> 5 Hundred No Conversion Required
Direction Ratio 3: 0.5 Hundred --> 0.5 Hundred No Conversion Required
Z Coordinate in 3D Space: 3 Hundred --> 3 Hundred No Conversion Required
Constant Coefficient of Plane1: 2 Hundred --> 2 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
L = modulus((a1*X)+(b2*Y)+(c3*Z)-(CoefConstant_plane1)) --> modulus((0.7*2)+(0.2*5)+(0.5*3)-(2))
Evaluating ... ...
L = 1.9
STEP 3: Convert Result to Output's Unit
1.9 Meter --> No Conversion Required
1.9 Meter <-- Length
(Calculation completed in 00.016 seconds)

## < 7 Distance in 3D space Calculators

Distance between two points in 3D space
distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2) Go
Distance between plane in normal formal and point
length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1)) Go
Distance between 2 parallel planes
length = (Constant Coefficient of Plane2-Constant Coefficient of Plane1)/((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2) Go
Distance of point from origin
distance_1 = sqrt((X1 Coordinate in 3D Space)^2+ (Y1 Coordinate in 3D Space)^2+ (Z1 Coordinate in 3D Space)^2) Go
Length of line given direction ratio and projection of line with x axis
length = (Projection of line)/(Direction Ratio 1) Go
Length of line given direction ratio and projection of line with y axis
length = (Projection of line)/(Direction Ratio 2) Go
Length of line given direction ratio and projection of line with z axis
length = (Projection of line)/(Direction Ratio 3) Go

### Distance between plane in normal formal and point Formula

length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1))
L = modulus((a1*X)+(b2*Y)+(c3*Z)-(CoefConstant_plane1))

## What is plane?

A plane is a surface such that, if two points are taken on it, a straight line joining them lies wholly in the surface. The coefficient of x, y and z in the cartesian equation of a plane are the direction ratios of normal to the plane.

## How to Calculate Distance between plane in normal formal and point?

Distance between plane in normal formal and point calculator uses length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1)) to calculate the Length, The Distance between plane in normal formal and point formula is defined as length measured from plane lx + my + nz = p and point. Length and is denoted by L symbol.

How to calculate Distance between plane in normal formal and point using this online calculator? To use this online calculator for Distance between plane in normal formal and point, enter Direction Ratio 1 (a1), X Coordinate in 3D Space (X), Direction Ratio 2 (b2), Y Coordinate in 3D Space (Y), Direction Ratio 3 (c3), Z Coordinate in 3D Space (Z) & Constant Coefficient of Plane1 (CoefConstant_plane1) and hit the calculate button. Here is how the Distance between plane in normal formal and point calculation can be explained with given input values -> 1.9 = modulus((0.7*2)+(0.2*5)+(0.5*3)-(2)).

### FAQ

What is Distance between plane in normal formal and point?
The Distance between plane in normal formal and point formula is defined as length measured from plane lx + my + nz = p and point and is represented as L = modulus((a1*X)+(b2*Y)+(c3*Z)-(CoefConstant_plane1)) or length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1)). Direction Ratio 1 is ratio proportional to direction cosine w.r.to x axis, X Coordinate in 3D Space is defined as the a point on x axis, Direction Ratio 2 is ratio proportional to direction cosine w.r.to y axis, Y Coordinate in 3D Space is defined as the a point on y axis, Direction Ratio 3 is ratio proportional to direction cosine w.r.to z axis, Z Coordinate in 3D Space is defined as the a point on z axis & Constant Coefficient of Plane1 is defined as a number which is constant in plane of form lx + my + nz = p.
How to calculate Distance between plane in normal formal and point?
The Distance between plane in normal formal and point formula is defined as length measured from plane lx + my + nz = p and point is calculated using length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1)). To calculate Distance between plane in normal formal and point, you need Direction Ratio 1 (a1), X Coordinate in 3D Space (X), Direction Ratio 2 (b2), Y Coordinate in 3D Space (Y), Direction Ratio 3 (c3), Z Coordinate in 3D Space (Z) & Constant Coefficient of Plane1 (CoefConstant_plane1). With our tool, you need to enter the respective value for Direction Ratio 1, X Coordinate in 3D Space, Direction Ratio 2, Y Coordinate in 3D Space, Direction Ratio 3, Z Coordinate in 3D Space & Constant Coefficient of Plane1 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Length?
In this formula, Length uses Direction Ratio 1, X Coordinate in 3D Space, Direction Ratio 2, Y Coordinate in 3D Space, Direction Ratio 3, Z Coordinate in 3D Space & Constant Coefficient of Plane1. We can use 7 other way(s) to calculate the same, which is/are as follows -
• length = (Projection of line)/(Direction Ratio 1)
• length = (Projection of line)/(Direction Ratio 2)
• length = (Projection of line)/(Direction Ratio 3)
• distance_1 = sqrt((X1 Coordinate in 3D Space)^2+ (Y1 Coordinate in 3D Space)^2+ (Z1 Coordinate in 3D Space)^2)
• length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1))
• length = (Constant Coefficient of Plane2-Constant Coefficient of Plane1)/((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)
• distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2) Let Others Know