Finding Vector v Given a, b, and c

[duoshikunli]

Homework Statement

The unknown vector v satisfies b . v = a and b x v = c, where a, b, and c are fixed and known. Find v in terms of a, b, and c.

Homework Equations

The Attempt at a Solution

 

[Char. Limit]

And what have you tried? Personally, I would start with finding the dot and cross products there...

 

[duoshikunli]

I understand dot and cross product. I've played with it a lot, mostly with cross product, but I'm not getting anywhere. I have a feeling that I'm suppose to manipulate it using some other trick. Can someone guide me in the right way?

 

[╔(σ_σ)╝]

Have you tried

$$b \cdot v = |b||v|cos \theta$$
$$| b \times v | = |b||v|sin \theta$$

 

[duoshikunli]

(|b||v|)^2 = a^2 + c^2
v . v = |v|^2 = (a^2 + c^2) / |b|^2

And I'm stuck...

 

[╔(σ_σ)╝]

(|b||v|)^2 = a^2 + c^2
v . v = |v|^2 = (a^2 + c^2) / |b|^2

And I'm stuck...

Check your work c^2 means nothing.
I assume you mean |c|^2.

A vector is uniquely determined by it's magnitude and direction.

You have |v| all you need now is a unit vector in v's direction.