# What is the angle between the body diagonal of a cube?

## What is the angle between the body diagonal of a cube?

Hint: To prove the angle between any two diagonals of the cube is cos−1(13), first we have to draw a diagram of the cube. After drawing the cube, we have to mark the coordinates and mark the points.

Are the body diagonals of a cube perpendicular?

A diagonal of a cube is a segment joining two points that are not the endpoints of an edge. The final edge is perpendicular in particular to the longest diagonal of the previous cube, and these two segments form the two sides of a right triangle having the longest diagonal of the new cube as its hypotenuse.

### What is the angle between two intersecting body diagonals of a cube a body diagonal connects two corners and passes through the interior of the cube?

The two diagonals cross at 90 degrees. You might intuitively guess that two diagonals of a cube, each running from one corner of the cube to its opposite corner and crossing in the center, would also cross at right angles.

How to find the main diagonal of a cube?

If we assume the cube has unit side length and lies in the first octant with faces parallel to the coordinate planes and one vertex at the origin, then the the vector ( 1, 1, 0) describes a diagonal of a face, and the vector ( 1, 1, 1) describes the skew diagonal. Thanks for contributing an answer to Mathematics Stack Exchange!

#### What’s the angle between the corners of a cube?

I was told it was 90 degrees, but then others say it is about 35.26 degrees. Now I am unsure which one it is. It depends on what you mean by the skew diagonal. Consider the cube with corners at ( x, y, z) where each element is either zero or one. In particular, one diagonal is 0 = ( 0, 0, 0) to u = ( 1, 1, 1).

How to find the angle between two diagonals?

On the other hand, if you mean a skew diagonal such as the diagonal from ( 1, 0, 0) and ( 0, 1, 0), then that vector of that diagonal is w = ( − 1, 1, 0), and u ⋅ w = 0 so the two angles are perpendicular.

## What is the inverse cosine of a skew diagonal?

In particular, one diagonal is 0 = ( 0, 0, 0) to u = ( 1, 1, 1). Now it depends on what you mean by a “skew diagonal.” The inverse cosine of that value is approximately 35.26 degrees.