Cross Product

Topics:

• Know how to compute the cross product of two vectors in ${\mathbb{R}}^3$.
• Be able to use a cross product to find a vector perpendicular to two given vectors.
• Know how to use a cross product to find areas of parallelograms and triangles.
• Be able to use a cross product together with a dot product to compute volumes of parallelepipeds.

To find a vector orthogonal to two vectors, take the cross product

$$\vec{a}\times \vec{b}=|a||b|\sin \theta \hat{n}$$

this is tautological, how do we get n?

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