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## PowerPoint Slideshow about ' MAT 1236 Calculus III' - cedric

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HW…

- WebAssign 12.4
- Read 12.5 (Seriously!): The first not too easy section in Calculus

Preview

- Define a new operation on vectors: The Cross Product
- Unlike the dot product, the cross product of two vectors is a vector.
- Properties of the cross product.

We are Interested in …

- Given 2 vectors, they “span” a plane
- Find a vector perpendicular to this plane

The Cross Product

If and , the cross product of a and b is the vector

The Cross Product

The formula is traditionally memorized by using (formal) determinant expansions

The Cross Product

The formula is traditionally memorized by using (formal) determinant expansions

Expectations

- You are expected to use the above standard procedure to find the cross product.
- You are expected to show all the steps. Keep in mind, good practices are key to minimize the chance of making mistakes.

Property B

In addition, the cross product obeys the Right Hand Rule.

In Particular

is in the same direction of k and

Property D

Two nonzero vectors and are parallel if and only if

Property D (Why?)

Two nonzero vectors and are parallel if and only if

Property E

The length of the cross product axb is equal to the area of the parallelogram

determined by a and b.

Example 2

Find a vector perpendicular to the plane that passes through the points

P(6,0,0) , Q(1,1,1), R(0,0,2)

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