- #1
dr721
- 23
- 0
Homework Statement
Given the nonzero vector a ε ℝ3, a[itex]\dot{}[/itex]x = b ε ℝ, and a × x = c ε ℝ3, can you determine the vector x ε ℝ3? 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!