What are the possible values for the coordinate angles in 3-D space?

In summary, the given options state that in 3-D coordinate space, any two of the coordinate angles must have cosines less than (√2/2) and a sum of less than 1. The formula cosα^2 + cosβ^2 + cosγ^2 = 1 supports this, as the sum of the squared cosines must equal 1. Therefore, the correct option for the vector given (cosines of 1, 0, 0) is e, as it satisfies both conditions.
  • #1
Tiven white
58
0
1. Homework Statement [/
In 3-D coordinate space, any two of the coordinate angles must …
Select one:
a. sum to less than 1
b. be greater than 90° but less than 180°
c. each be greater than 45°
d. sum to greater than 90° (if they are both less than 90°).
e. have cosines less than (√2/2).

Homework Equations



(cosα(α))^2 + (cos(β))^2 + (cos(γ))^2 = 1

3. The Attempt at a Solution .

since the sum of the squared cosine of alpha beta and gamma = 1 the answer to me is e reason being if the value of the cosine of the angle is (√2/2) then the square = 0.5 and the sum of two of these angles = 1 therefore the cosine has to be less than (√2/2). c could also be an option since all angles with (√2/2) is greater than 45°. but when i tried with example 150° for both angles the cosine is > than (√2/2) but negative. but when squared it is positive which implies the sum of the two would be greater than 1 and denounces 'c' is 'e' then the required solution.
 
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  • #2
Consider a simple vector given by cosines (1, 0, 0). This is simply a unit vector directed along the X axis. Is either C or E true for it?
 

Related to What are the possible values for the coordinate angles in 3-D space?

1. What are 3D coordinate angles α β γ?

3D coordinate angles α β γ refer to the angles formed by three intersecting planes in three-dimensional space. These angles are measured using the Greek letters α, β, and γ and are used to determine the orientation of an object or point in space.

2. How are 3D coordinate angles α β γ represented?

3D coordinate angles α β γ are typically represented using a right-handed coordinate system, where α represents the angle between the x-axis and the projected line on the xy-plane, β represents the angle between the y-axis and the projected line on the yz-plane, and γ represents the angle between the z-axis and the projected line on the xz-plane.

3. What is the range of values for 3D coordinate angles α β γ?

The range of values for 3D coordinate angles α β γ is from 0 degrees to 360 degrees. These angles can also be expressed in radians, with the range being from 0 to 2π radians.

4. How are 3D coordinate angles α β γ used in computer graphics?

3D coordinate angles α β γ are used in computer graphics to determine the orientation and rotation of 3D objects. They are also used in creating 3D animations and simulations, as well as in video game development.

5. What is the relationship between 3D coordinate angles α β γ and 2D coordinate angles?

The relationship between 3D coordinate angles α β γ and 2D coordinate angles is that they both represent the orientation of an object or point in space. However, 3D coordinate angles have an extra dimension and are used to determine the orientation in three-dimensional space, while 2D coordinate angles are used in two-dimensional space.

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