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# MAT 1236 Calculus III - PowerPoint PPT Presentation

MAT 1236 Calculus III. Section 12.4 The Cross Product. http://myhome.spu.edu/lauw. 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

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### MAT 1236Calculus III

Section 12.4

The Cross Product

http://myhome.spu.edu/lauw

• WebAssign 12.4

• Read 12.5 (Seriously!): The first not too easy section in Calculus

• 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.

• Given 2 vectors, they “span” a plane

• Find a vector perpendicular to this plane

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

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

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

• 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.

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

is in the same direction of k and

Two nonzero vectors and are parallel if and only if

Two nonzero vectors and are parallel if and only if

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

determined by a and b.

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

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

Find the area of the triangle with vertices

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

Right Hand Rule

Default

Reference only