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Dot Product (Scalar Product)

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Dot Product (Scalar Product)

This product of two vectors results in a scalar quantity. You multiply one vector by the component of the second vector that is parallel to the first vector.

If A = B: We use the same rules when multiplying a vector by itself.

The square of a vector only gives magnitude.

Example: Determine the angle between the vectors A and B.

Vector Product (Cross-product)

There are two different methods for determining the vector product between any two vectors: The Determinant method and the Cyclic method

Determinant Method

Cyclic Method

Rewrite the j term as to get an identical expression

The direction of the resultant vector, for a right-handed coordinate system, for a vector product can be determined using the right-hand rule.

Fingers point in the direction of the second vector

The vector product looks at the product of two vectors which are perpendicular to each other, and who are also perpendicular to the resultant vector.

Thumb points in the direction of first vector.

Palm points in the direction of resultant vector.

Example: Determine the magnitude and direction of the area of a parallelogram described by the vectors r1 and r2 which are used to describe the length of the two sides.

y

r1

r2

x

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