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Walchand College of Engineering (WCE), Sangli
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## Direction cosine of line 1 with z axis given angle between line 1 and 2 Solution

STEP 0: Pre-Calculation Summary
Formula Used
direction_cosine_1_with_respect_to_z_axis = cos(Angle A)-(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 2 with respect to z axis)
n1 = cos(∠A)-(l1*l2)-(m1*m2)/(n2)
This formula uses 1 Functions, 6 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
Variables Used
Angle A - The angle A the space between two intersecting lines or surfaces at or close to the point where they meet. (Measured in Degree)
Direction cosine 1 with respect to x axis - Direction cosine 1 with respect to x axis is the cosine of angle made by a line w.r.to x axis. (Measured in Hundred)
Direction cosine 2 with respect to x axis - Direction cosine 2 with respect to x axis is the cosine of angle made by a line w.r.to x axis. (Measured in Hundred)
Direction cosine 1 with respect to y axis - Direction cosine 1 with respect to y axis is the cosine of angle made by a line w.r.to y axis. (Measured in Hundred)
Direction cosine 2 with respect to y axis - Direction cosine 2 with respect to y axis is the cosine of angle made by a line w.r.to y axis. (Measured in Hundred)
Direction cosine 2 with respect to z axis - Direction cosine 2 with respect to z axis is the cosine of angle made by a line w.r.to z axis. (Measured in Hundred)
STEP 1: Convert Input(s) to Base Unit
Angle A: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Direction cosine 1 with respect to x axis: 0.7 Hundred --> 0.7 Hundred No Conversion Required
Direction cosine 2 with respect to x axis: 0.7 Hundred --> 0.7 Hundred No Conversion Required
Direction cosine 1 with respect to y axis: 0.8 Hundred --> 0.8 Hundred No Conversion Required
Direction cosine 2 with respect to y axis: 0.6 Hundred --> 0.6 Hundred No Conversion Required
Direction cosine 2 with respect to z axis: 0.6 Hundred --> 0.6 Hundred No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
n1 = cos(∠A)-(l1*l2)-(m1*m2)/(n2) --> cos(0.5235987755982)-(0.7*0.7)-(0.8*0.6)/(0.6)
Evaluating ... ...
n1 = -0.423974596215561
STEP 3: Convert Result to Output's Unit
-0.423974596215561 Hundred --> No Conversion Required
-0.423974596215561 Hundred <-- Direction cosine 1 with respect to z axis
(Calculation completed in 00.015 seconds)

## < 9 Direction cosine of line in 3D Space Calculators

Direction cosine of line 2 with x axis given angle between line 1 and 2
direction_cosine_2_with_respect_to_x_axis = (cos(Angle A)-(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))/(Direction cosine 1 with respect to x axis) Go
Direction cosine of line 1 with x axis given angle between line 1 and 2
direction_cosine_1_with_respect_to_x_axis = (cos(Angle A)-(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))/(Direction cosine 2 with respect to x axis) Go
Direction cosine of line 2 with y axis given angle between line 1 and 2
direction_cosine_2_with_respect_to_y_axis = cos(Angle A)-(Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to z axis)/(Direction cosine 1 with respect to y axis) Go
Direction cosine of line 2 with z axis given angle between line 1 and 2
direction_cosine_2_with_respect_to_z_axis = cos(Angle A)-(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) Go
Direction cosine of line 1 with z axis given angle between line 1 and 2
direction_cosine_1_with_respect_to_z_axis = cos(Angle A)-(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 2 with respect to z axis) Go
Direction cosine of line 1 with y axis given angle between line 1 and 2
direction_cosine_1_with_respect_to_y_axis = cos(Angle A)-(Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to z axis)/(Direction cosine 2 with respect to y axis) Go
Direction cosine of line with z axis
direction_cosine_with_respect_to_z_axis = cos(Angle C) Go
Direction cosine of line with x axis
direction_cosine_with_respect_to_x_axis = cos(Angle A) Go
Direction cosine of line with y axis
direction_cosine_with_respect_to_y_axis = cos(Angle B) Go

### Direction cosine of line 1 with z axis given angle between line 1 and 2 Formula

direction_cosine_1_with_respect_to_z_axis = cos(Angle A)-(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 2 with respect to z axis)
n1 = cos(∠A)-(l1*l2)-(m1*m2)/(n2)

## What is coordinate system in 3D space?

The three mutually perpendicular lines in a space which divides the space into eight parts and if these perpendicular lines are the coordinate axes, then it is said to be a coordinate system.

## How to Calculate Direction cosine of line 1 with z axis given angle between line 1 and 2?

Direction cosine of line 1 with z axis given angle between line 1 and 2 calculator uses direction_cosine_1_with_respect_to_z_axis = cos(Angle A)-(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 2 with respect to z axis) to calculate the Direction cosine 1 with respect to z axis, Direction cosine of line 1 with z axis given angle between line 1 and 2 is defined as cosine of angle formed by line 1 with z axis and other line. Direction cosine 1 with respect to z axis and is denoted by n1 symbol.

How to calculate Direction cosine of line 1 with z axis given angle between line 1 and 2 using this online calculator? To use this online calculator for Direction cosine of line 1 with z axis given angle between line 1 and 2, enter Angle A (∠A), Direction cosine 1 with respect to x axis (l1), Direction cosine 2 with respect to x axis (l2), Direction cosine 1 with respect to y axis (m1), Direction cosine 2 with respect to y axis (m2) & Direction cosine 2 with respect to z axis (n2) and hit the calculate button. Here is how the Direction cosine of line 1 with z axis given angle between line 1 and 2 calculation can be explained with given input values -> -0.423975 = cos(0.5235987755982)-(0.7*0.7)-(0.8*0.6)/(0.6).

### FAQ

What is Direction cosine of line 1 with z axis given angle between line 1 and 2?
Direction cosine of line 1 with z axis given angle between line 1 and 2 is defined as cosine of angle formed by line 1 with z axis and other line and is represented as n1 = cos(∠A)-(l1*l2)-(m1*m2)/(n2) or direction_cosine_1_with_respect_to_z_axis = cos(Angle A)-(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 2 with respect to z axis). The angle A the space between two intersecting lines or surfaces at or close to the point where they meet, Direction cosine 1 with respect to x axis is the cosine of angle made by a line w.r.to x axis, Direction cosine 2 with respect to x axis is the cosine of angle made by a line w.r.to x axis, Direction cosine 1 with respect to y axis is the cosine of angle made by a line w.r.to y axis, Direction cosine 2 with respect to y axis is the cosine of angle made by a line w.r.to y axis & Direction cosine 2 with respect to z axis is the cosine of angle made by a line w.r.to z axis.
How to calculate Direction cosine of line 1 with z axis given angle between line 1 and 2?
Direction cosine of line 1 with z axis given angle between line 1 and 2 is defined as cosine of angle formed by line 1 with z axis and other line is calculated using direction_cosine_1_with_respect_to_z_axis = cos(Angle A)-(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 2 with respect to z axis). To calculate Direction cosine of line 1 with z axis given angle between line 1 and 2, you need Angle A (∠A), Direction cosine 1 with respect to x axis (l1), Direction cosine 2 with respect to x axis (l2), Direction cosine 1 with respect to y axis (m1), Direction cosine 2 with respect to y axis (m2) & Direction cosine 2 with respect to z axis (n2). With our tool, you need to enter the respective value for Angle A, 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 2 with respect to z axis 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 Direction cosine 1 with respect to z axis?
In this formula, Direction cosine 1 with respect to z axis uses Angle A, 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 2 with respect to z axis. We can use 9 other way(s) to calculate the same, which is/are as follows -
• direction_cosine_with_respect_to_z_axis = cos(Angle C)
• direction_cosine_with_respect_to_x_axis = cos(Angle A)
• direction_cosine_2_with_respect_to_x_axis = (cos(Angle A)-(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))/(Direction cosine 1 with respect to x axis)
• direction_cosine_1_with_respect_to_x_axis = (cos(Angle A)-(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))/(Direction cosine 2 with respect to x axis)
• direction_cosine_2_with_respect_to_z_axis = cos(Angle A)-(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_y_axis = cos(Angle A)-(Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to z axis)/(Direction cosine 1 with respect to y axis)
• direction_cosine_1_with_respect_to_z_axis = cos(Angle A)-(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 2 with respect to z axis)
• direction_cosine_1_with_respect_to_y_axis = cos(Angle A)-(Direction cosine 1 with respect to x axis*Direction cosine 2 with respect to x axis)-(Direction cosine 1 with respect to z axis*Direction cosine 2 with respect to z axis)/(Direction cosine 2 with respect to y axis)
• direction_cosine_with_respect_to_y_axis = cos(Angle B) Let Others Know