- #1

dr721

- 23

- 0

## Homework Statement

Given the nonzero vector

**a**ε ℝ

^{3},

**a**[itex]\dot{}[/itex]

**x**= b ε ℝ, and

**a**×

**x**=

**c**ε ℝ

^{3}, can you determine the vector

**x**ε ℝ

^{3}? If so, give a geometric construction for

**x**.

## Homework Equations

**a**[itex]\dot{}[/itex]

**x**= ||

**a**||||

**x**||cos[itex]\Theta[/itex]

## The Attempt at a Solution

I'm not really certain what it is asking for?

Obviously, the cross product of the two vectors creates a vector perpendicular to all vectors in the a, x plane. And, the magnitude of the cross product defines the area of a parallelogram spanned by a and x.

Also, ||

**x**||cos[itex]\Theta[/itex] is the length of the projection of x onto a, which is also equal to b/||

**a**||

But while I know all this, I don't know what I'm trying to show or how to show it?

Any help would be great! Thanks!