# Angle between A & B: 35.26 degrees or 90 degrees?

• jrevard
That vector would be {(1,1,0), (0,0,-1)} which has the correct magnitude but the wrong direction. In summary, the problem involves finding vectors on a cube and their cross product, with a discrepancy in the reported answer for the angle between two vectors.
jrevard
This is from an advanced physics book, but is one of the first problems in the first chapter and only deals with vectors. The reported answer and mine do not coincide. For part (d) I get 35.26 degrees, the reported answer is 90 degrees. (Note: all variables are vectors)

## Homework Statement

Consider a cube whose edges are each of unit length. One corner coincides with the origin of an xyz Cartesian coordinate system. Three of the cube's edges extend from the origin along the positive direction of each coordinate axis. Find the vector that begins at the origin and extends
(a) along a major diagonal of the cube;
(b) along the diagonal of the lower face of the cube.
(c) Calling these vectors A and B, find C = A x B.
(d) Find the angle between A and B

## Homework Equations

cos(theta) = (A dot B)/(|A||B|)

## The Attempt at a Solution

I get cos(theta) = 2/(root(6)),

they get cos(theta) = (1-1)/(root(6)) = 0

From the wording of the problem, I would say that you are correct.

From the book's solution, it looks like they took the diagonal of the lower face that doesn't start (nor end) at the origin.

## 1. What is the difference between an angle of 35.26 degrees and an angle of 90 degrees?

An angle of 35.26 degrees is smaller than an angle of 90 degrees. The difference between the two angles is 54.74 degrees.

## 2. How do I determine the angle between two lines if I know the angle between them is 35.26 degrees or 90 degrees?

To determine the angle between two lines, you can use the angle between lines formula, which states that the angle between two lines is equal to the inverse cosine of the dot product of the two lines. For an angle of 35.26 degrees, the dot product would be 0.82, and for an angle of 90 degrees, the dot product would be 0.

## 3. Can the angle between two lines be negative?

No, the angle between two lines cannot be negative. The angle between two lines is always measured as a positive value between 0 and 180 degrees.

## 4. How can I visualize an angle of 35.26 degrees or 90 degrees?

To visualize an angle of 35.26 degrees, you can imagine a clock where the minute hand is pointing at the 7 and the hour hand is pointing at the 12. This creates an angle of 35.26 degrees. To visualize an angle of 90 degrees, you can imagine the minute hand pointing at the 3 and the hour hand pointing at the 12 on a clock, creating a right angle.

## 5. Is the angle between two lines always constant?

No, the angle between two lines can vary depending on the orientation of the lines. For example, if one line is rotated while the other stays in the same position, the angle between them will change. However, if both lines are rotated by the same amount, the angle between them will remain constant.

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