Direction of cartesian equation

[goldfish9776]

Homework Statement

In this question, I didn't see why the given 90 degree is 90 degree becoz it doesn't look like 90 degree. Can someone draw me a better diagram? It's hard to visualize it's 90 degree

Homework Equations

The Attempt at a Solution

 

[paisiello2]

Well it's trying to represent an angle measured in a 2D plane in 3D space on a 2D piece of paper. So it will always look skewed when the plane is not the same as the plane of the paper.

 

[RUber]

They are trying to illustrate the 90 degree angles in 3D space. A common way to visualize this is to subractthe Z component, and you will clearly see the right angles in the x-y plane.

The angles are 90 degrees by definition. You should not question it just because when it is illustrated at a skew angle it doesn't look like the square angle you are used to.

The method being used is one that involves drawing a perpendicular line from the end of A to whichever axis you are interested in. Since your new coordinates are defined with angles to the vector A from a given axis, the definitions are given in terms of cosine(angle) = adjacent (axis) divided by magnitude (vector).

 

[goldfish9776]

They are trying to illustrate the 90 degree angles in 3D space. A common way to visualize this is to subractthe Z component, and you will clearly see the right angles in the x-y plane.

The angles are 90 degrees by definition. You should not question it just because when it is illustrated at a skew angle it doesn't look like the square angle you are used to.

The method being used is one that involves drawing a perpendicular line from the end of A to whichever axis you are interested in. Since your new coordinates are defined with angles to the vector A from a given axis, the definitions are given in terms of cosine(angle) = adjacent (axis) divided by magnitude (vector).

well , i still don't understand . take an example , alpha already more than 90 degree. How can the other angle be 90 degree? Can you explain in other words , so that i can understand better ?

 

[SteamKing]

well , i still don't understand . take an example , alpha already more than 90 degree. How can the other angle be 90 degree? Can you explain in other words , so that i can understand better ?

How do you know alpha is more than 90° ? Remember, these are not plane triangles you are looking at. They are triangles in three dimensions which are drawn on a two-dimensional page.

A better way to look at these diagrams is to imagine that the right angles are showing that there are three planes which are parallel to the x-y plane, the y-z plane and the x-z plane and which are also perpendicular to one another.

 

[insightful]

I suggest you cut a corner off a piece of paper and view it at different angles to replicate the drawing views.