- #1

- 202

- 0

Suppose you have three vectors

**a**,

**b**and

**c**.

Say the angle between

**a**and

**c**is given by [tex]\alpha[/tex], and between

**b**and

**c**by [tex]\beta[/tex].

Can we find a relationship between [tex]\alpha[/tex] and [tex]\beta[/tex]?

Thanks in advance,

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- Thread starter Apteronotus
- Start date

- #1

- 202

- 0

Suppose you have three vectors

Say the angle between

Can we find a relationship between [tex]\alpha[/tex] and [tex]\beta[/tex]?

Thanks in advance,

- #2

- 166

- 0

[tex]a . c = ||a|| ||c|| cos(\alpha)[/tex]

[tex]b . c = ||b|| ||c|| cos(\beta)[/tex]

So you could rearrange that to find a relationship between [tex]\alpha[/tex] and [tex]\beta[/tex].

- #3

- 202

- 0

Of course you are correct. But I'm wondering can a relation be found that does not involve the dot product? Perhaps if we think of the three vectors as the edge of a parallelepiped?

- #4

- 166

- 0

Of course you are correct. But I'm wondering can a relation be found that does not involve the dot product? Perhaps if we think of the three vectors as the edge of a parallelepiped?

Even if you are defining a parallelepiped in 3space, I don't think you can escape from the notion of dot and cross products. Looking at a http://upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Parallelepiped_volume.svg/780px-Parallelepiped_volume.svg.png" [Broken] of it, it seems unavoidable to me.

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