Finding the magnitude of a vector product between two vectors?

Question

Vector $\overrightarrow{A}$ has magnitude $11.0m$ and vector $\overrightarrow{B}$ has magnitude $16.0m$ . The scalar product $\overrightarrow{A}\bullet \overrightarrow{B}$ is $79.0m^2$.

What is the magnitude of the vector product between these two vectors?

I'm not exactly sure how to get started with this problem and would appreciate tips just to get me going.

Answer 1

A quick way to get it:

You know the lengths of the two vectors and that $ \ \vec{A} \bullet \vec{B} \ $ is given by $ || \vec{A} || \cdot || \vec{B} || \ \cos \theta \ $ . The magnitude of $ \ \vec{A} \ \times \ \vec{B} \ $ is $ || \vec{A} || \cdot || \vec{B} || \ \sin \theta \ , $ so find $ \ \cos \theta \ $ and use $ \ \sin \theta \ = \ \sqrt{1 - \cos^2 \theta} \ $ .

Answer 2

Hint: $\sin^{2}\theta=1-\cos^{2}\theta$
Further Hint: $|\vec{A} \cdot \vec{B}|=|\vec{A}| |\vec{B}|\cos\theta$ and $|\vec{A} \times \vec{B}|=|\vec{A}||\vec{B}|\sin\theta$