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## Angle between line and plane given coefficients of line and plane Solution

STEP 0: Pre-Calculation Summary
Formula Used
angle_a = asin(((Direction ratio 1 of line1*Direction Ratio 1)+(Direction ratio 2 of line1*Direction Ratio 2)+(Direction ratio 3 of line1*Direction Ratio 3))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)))
∠A = asin(((a1_line1*a1)+(b2_line1*b2)+(c3_line1*c3))/(sqrt((a1_line1)^2+(b2_line1)^2+(c3_line1)^2))*(sqrt((a1)^2+(b2)^2+(c3)^2)))
This formula uses 3 Functions, 6 Variables
Functions Used
sin - Trigonometric sine function, sin(Angle)
asin - Inverse trigonometric sine function, asin(Number)
sqrt - Squre root function, sqrt(Number)
Variables Used
Direction ratio 1 of line1 - Direction ratio 1 of line1 is defined as the quotient of two x coordinates of line1. (Measured in Hundred)
Direction Ratio 1 - Direction Ratio 1 is ratio proportional to direction cosine w.r.to x axis. (Measured in Hundred)
Direction ratio 2 of line1 - Direction ratio 2 of line1 is defined as the quotient of two y coordinates of line 1. (Measured in Hundred)
Direction Ratio 2- Direction Ratio 2 is ratio proportional to direction cosine w.r.to y axis.
Direction ratio 3 of line1 - Direction ratio 3 of line1 is defined as the quotient of two z coordinates of line 1. (Measured in Hundred)
Direction Ratio 3 - Direction Ratio 3 is ratio proportional to direction cosine w.r.to z axis. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
Direction ratio 1 of line1: 0.2 Hundred --> 0.2 Hundred No Conversion Required
Direction Ratio 1: 0.7 Hundred --> 0.7 Hundred No Conversion Required
Direction ratio 2 of line1: 0.5 Hundred --> 0.5 Hundred No Conversion Required
Direction Ratio 2: 0.2 --> No Conversion Required
Direction ratio 3 of line1: 0.7 Hundred --> 0.7 Hundred No Conversion Required
Direction Ratio 3: 0.5 Hundred --> 0.5 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
∠A = asin(((a1_line1*a1)+(b2_line1*b2)+(c3_line1*c3))/(sqrt((a1_line1)^2+(b2_line1)^2+(c3_line1)^2))*(sqrt((a1)^2+(b2)^2+(c3)^2))) --> asin(((0.2*0.7)+(0.5*0.2)+(0.7*0.5))/(sqrt((0.2)^2+(0.5)^2+(0.7)^2))*(sqrt((0.7)^2+(0.2)^2+(0.5)^2)))
Evaluating ... ...
∠A = 0.631058840778021
STEP 3: Convert Result to Output's Unit
0.631058840778021 Radian -->36.1570082010056 Degree (Check conversion here)
36.1570082010056 Degree <-- Angle A
(Calculation completed in 00.015 seconds)

## < 4 Angle in 3D space Calculators

Angle between two planes
angle_c = acos(((Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to x axis)+(Direction cosine 1 with respect to y axis*Direction cosine 2 with respect to y axis)+(Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to z axis))/(sqrt((Direction cosine 1 with respect to x axis)^2+(Direction cosine 1 with respect to y axis)^2+(Direction cosine 1 with respect to z axis)^2)* sqrt((Direction cosine 2 with respect to x axis)^2+(Direction cosine 2 with respect to y axis)^2+(Direction cosine 2 with respect to z axis)^2))) Go
Angle made by direction cosines of two lines in sine form
angle = asin(sqrt(((Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to y axis)- (Direction cosine 2 with respect to x axis*Direction cosine 1 with respect to y axis))^2+((Direction cosine 1 with respect to y axis*Direction cosine 2 with respect to z axis)-(Direction cosine 2 with respect to y axis*Direction cosine 1 with respect to z axis))^2+((Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to x axis)-(Direction cosine 2 with respect to z axis*Direction cosine 1 with respect to x axis))^2)) Go
Angle between two lines given direction ratios of two lines
angle_b = acos(((Direction ratio 1 of line1*Direction ratio 1 of line2)+(Direction ratio 2 of line1*Direction ratio 2 of line2)+(Direction ratio 3 of line1*Direction ratio 3 of line2))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction ratio 1 of line2)^2+(Direction ratio 2 of line2)^2+(Direction ratio 3 of line2)^2))) Go
Angle between line and plane given coefficients of line and plane
angle_a = asin(((Direction ratio 1 of line1*Direction Ratio 1)+(Direction ratio 2 of line1*Direction Ratio 2)+(Direction ratio 3 of line1*Direction Ratio 3))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2))) Go

### Angle between line and plane given coefficients of line and plane Formula

angle_a = asin(((Direction ratio 1 of line1*Direction Ratio 1)+(Direction ratio 2 of line1*Direction Ratio 2)+(Direction ratio 3 of line1*Direction Ratio 3))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)))
∠A = asin(((a1_line1*a1)+(b2_line1*b2)+(c3_line1*c3))/(sqrt((a1_line1)^2+(b2_line1)^2+(c3_line1)^2))*(sqrt((a1)^2+(b2)^2+(c3)^2)))

## 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 Angle between line and plane given coefficients of line and plane?

Angle between line and plane given coefficients of line and plane calculator uses angle_a = asin(((Direction ratio 1 of line1*Direction Ratio 1)+(Direction ratio 2 of line1*Direction Ratio 2)+(Direction ratio 3 of line1*Direction Ratio 3))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2))) to calculate the Angle A, The Angle between line and plane given coefficients of line and plane formula is defined as the angle made by line x – x1 / a1 = y – y1 / b1 = z – z1 / c1 and plane a2x + b2y + c2z + d2 = 0 form, (eg. direction_ratio_1 is of plane). Angle A and is denoted by ∠A symbol.

How to calculate Angle between line and plane given coefficients of line and plane using this online calculator? To use this online calculator for Angle between line and plane given coefficients of line and plane, enter Direction ratio 1 of line1 (a1_line1), Direction Ratio 1 (a1), Direction ratio 2 of line1 (b2_line1), Direction Ratio 2 (b2), Direction ratio 3 of line1 (c3_line1) & Direction Ratio 3 (c3) and hit the calculate button. Here is how the Angle between line and plane given coefficients of line and plane calculation can be explained with given input values -> 36.15701 = asin(((0.2*0.7)+(0.5*0.2)+(0.7*0.5))/(sqrt((0.2)^2+(0.5)^2+(0.7)^2))*(sqrt((0.7)^2+(0.2)^2+(0.5)^2))).

### FAQ

What is Angle between line and plane given coefficients of line and plane?
The Angle between line and plane given coefficients of line and plane formula is defined as the angle made by line x – x1 / a1 = y – y1 / b1 = z – z1 / c1 and plane a2x + b2y + c2z + d2 = 0 form, (eg. direction_ratio_1 is of plane) and is represented as ∠A = asin(((a1_line1*a1)+(b2_line1*b2)+(c3_line1*c3))/(sqrt((a1_line1)^2+(b2_line1)^2+(c3_line1)^2))*(sqrt((a1)^2+(b2)^2+(c3)^2))) or angle_a = asin(((Direction ratio 1 of line1*Direction Ratio 1)+(Direction ratio 2 of line1*Direction Ratio 2)+(Direction ratio 3 of line1*Direction Ratio 3))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2))). Direction ratio 1 of line1 is defined as the quotient of two x coordinates of line1, Direction Ratio 1 is ratio proportional to direction cosine w.r.to x axis, Direction ratio 2 of line1 is defined as the quotient of two y coordinates of line 1, Direction Ratio 2 is ratio proportional to direction cosine w.r.to y axis, Direction ratio 3 of line1 is defined as the quotient of two z coordinates of line 1 & Direction Ratio 3 is ratio proportional to direction cosine w.r.to z axis.
How to calculate Angle between line and plane given coefficients of line and plane?
The Angle between line and plane given coefficients of line and plane formula is defined as the angle made by line x – x1 / a1 = y – y1 / b1 = z – z1 / c1 and plane a2x + b2y + c2z + d2 = 0 form, (eg. direction_ratio_1 is of plane) is calculated using angle_a = asin(((Direction ratio 1 of line1*Direction Ratio 1)+(Direction ratio 2 of line1*Direction Ratio 2)+(Direction ratio 3 of line1*Direction Ratio 3))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2))). To calculate Angle between line and plane given coefficients of line and plane, you need Direction ratio 1 of line1 (a1_line1), Direction Ratio 1 (a1), Direction ratio 2 of line1 (b2_line1), Direction Ratio 2 (b2), Direction ratio 3 of line1 (c3_line1) & Direction Ratio 3 (c3). With our tool, you need to enter the respective value for Direction ratio 1 of line1, Direction Ratio 1, Direction ratio 2 of line1, Direction Ratio 2, Direction ratio 3 of line1 & Direction Ratio 3 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 Angle A?
In this formula, Angle A uses Direction ratio 1 of line1, Direction Ratio 1, Direction ratio 2 of line1, Direction Ratio 2, Direction ratio 3 of line1 & Direction Ratio 3. We can use 4 other way(s) to calculate the same, which is/are as follows -
• angle = asin(sqrt(((Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to y axis)- (Direction cosine 2 with respect to x axis*Direction cosine 1 with respect to y axis))^2+((Direction cosine 1 with respect to y axis*Direction cosine 2 with respect to z axis)-(Direction cosine 2 with respect to y axis*Direction cosine 1 with respect to z axis))^2+((Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to x axis)-(Direction cosine 2 with respect to z axis*Direction cosine 1 with respect to x axis))^2))
• angle_b = acos(((Direction ratio 1 of line1*Direction ratio 1 of line2)+(Direction ratio 2 of line1*Direction ratio 2 of line2)+(Direction ratio 3 of line1*Direction ratio 3 of line2))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction ratio 1 of line2)^2+(Direction ratio 2 of line2)^2+(Direction ratio 3 of line2)^2)))
• angle_a = asin(((Direction ratio 1 of line1*Direction Ratio 1)+(Direction ratio 2 of line1*Direction Ratio 2)+(Direction ratio 3 of line1*Direction Ratio 3))/(sqrt((Direction ratio 1 of line1)^2+(Direction ratio 2 of line1)^2+(Direction ratio 3 of line1)^2))*(sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)))
• angle_c = acos(((Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to x axis)+(Direction cosine 1 with respect to y axis*Direction cosine 2 with respect to y axis)+(Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to z axis))/(sqrt((Direction cosine 1 with respect to x axis)^2+(Direction cosine 1 with respect to y axis)^2+(Direction cosine 1 with respect to z axis)^2)* sqrt((Direction cosine 2 with respect to x axis)^2+(Direction cosine 2 with respect to y axis)^2+(Direction cosine 2 with respect to z axis)^2))) Let Others Know