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Direction cosine of z axis given direction ratio of x, y and z axis Solution

STEP 0: Pre-Calculation Summary
Formula Used
direction_cosine_1_with_respect_to_z_axis = (Direction Ratio 3)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)
n1 = (c3)/sqrt((a1)^2+(b2)^2+(c3)^2)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Direction Ratio 3 - Direction Ratio 3 is ratio proportional to direction cosine w.r.to z axis. (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- Direction Ratio 2 is ratio proportional to direction cosine w.r.to y axis.
STEP 1: Convert Input(s) to Base Unit
Direction Ratio 3: 0.5 Hundred --> 0.5 Hundred No Conversion Required
Direction Ratio 1: 0.7 Hundred --> 0.7 Hundred No Conversion Required
Direction Ratio 2: 0.2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
n1 = (c3)/sqrt((a1)^2+(b2)^2+(c3)^2) --> (0.5)/sqrt((0.7)^2+(0.2)^2+(0.5)^2)
Evaluating ... ...
n1 = 0.566138517072298
STEP 3: Convert Result to Output's Unit
0.566138517072298 Hundred --> No Conversion Required
FINAL ANSWER
0.566138517072298 Hundred <-- Direction cosine 1 with respect to z axis
(Calculation completed in 00.000 seconds)

3 Direction cosine in 3D Space Calculators

Direction cosine of x axis given direction ratio of x, y and z axis
direction_cosine_1_with_respect_to_x_axis = (Direction Ratio 1)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2) Go
Direction cosine of y axis given direction ratio of x, y and z axis
direction_cosine_1_with_respect_to_y_axis = (Direction Ratio 2)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2) Go
Direction cosine of z axis given direction ratio of x, y and z axis
direction_cosine_1_with_respect_to_z_axis = (Direction Ratio 3)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2) Go

Direction cosine of z axis given direction ratio of x, y and z axis Formula

direction_cosine_1_with_respect_to_z_axis = (Direction Ratio 3)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)
n1 = (c3)/sqrt((a1)^2+(b2)^2+(c3)^2)

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 z axis given direction ratio of x, y and z axis?

Direction cosine of z axis given direction ratio of x, y and z axis calculator uses direction_cosine_1_with_respect_to_z_axis = (Direction Ratio 3)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2) to calculate the Direction cosine 1 with respect to z axis, Direction cosine of z axis given direction ratio of x, y and z axis is defined as the ratio proportional to cosine of angle made by a line w.r.to z axis. Direction cosine 1 with respect to z axis and is denoted by n1 symbol.

How to calculate Direction cosine of z axis given direction ratio of x, y and z axis using this online calculator? To use this online calculator for Direction cosine of z axis given direction ratio of x, y and z axis, enter Direction Ratio 3 (c3), Direction Ratio 1 (a1) & Direction Ratio 2 (b2) and hit the calculate button. Here is how the Direction cosine of z axis given direction ratio of x, y and z axis calculation can be explained with given input values -> 0.566139 = (0.5)/sqrt((0.7)^2+(0.2)^2+(0.5)^2).

FAQ

What is Direction cosine of z axis given direction ratio of x, y and z axis?
Direction cosine of z axis given direction ratio of x, y and z axis is defined as the ratio proportional to cosine of angle made by a line w.r.to z axis and is represented as n1 = (c3)/sqrt((a1)^2+(b2)^2+(c3)^2) or direction_cosine_1_with_respect_to_z_axis = (Direction Ratio 3)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2). Direction Ratio 3 is ratio proportional to direction cosine w.r.to z axis, Direction Ratio 1 is ratio proportional to direction cosine w.r.to x axis & Direction Ratio 2 is ratio proportional to direction cosine w.r.to y axis.
How to calculate Direction cosine of z axis given direction ratio of x, y and z axis?
Direction cosine of z axis given direction ratio of x, y and z axis is defined as the ratio proportional to cosine of angle made by a line w.r.to z axis is calculated using direction_cosine_1_with_respect_to_z_axis = (Direction Ratio 3)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2). To calculate Direction cosine of z axis given direction ratio of x, y and z axis, you need Direction Ratio 3 (c3), Direction Ratio 1 (a1) & Direction Ratio 2 (b2). With our tool, you need to enter the respective value for Direction Ratio 3, Direction Ratio 1 & Direction Ratio 2 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 Direction Ratio 3, Direction Ratio 1 & Direction Ratio 2. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • direction_cosine_1_with_respect_to_x_axis = (Direction Ratio 1)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)
  • direction_cosine_1_with_respect_to_y_axis = (Direction Ratio 2)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)
  • direction_cosine_1_with_respect_to_z_axis = (Direction Ratio 3)/sqrt((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)
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