1.5.1 The Vector Product

Question 1

The Vector Product

Answer 1

• The vector product of two vectors and is another vector with magnitude . Its direction is perpendicular to both and and can be found using the right-hand rule.
• The vector product of and also represents the area of the parallelogram formed by the vectors.

Question 2

note

Answer 2

• When you take the scalar product of two vectors, the result is a scalar. There is another way to define the multiplication of vectors so that the result is a vector. This is called the vector product, or cross product, and it is denoted with across . The equation to the left defines the magnitude of the vector product of two vectors and .
• To understand why the factor of is in this definition, think about trying to loosen a bolt by applying a force to the end of a wrench. There are two vectors involved, a displacement vector from the bolt to the point where you are applying the force, and a vector for the force applied.
• The point is that the component of force that is parallel to the displacement vector is useless—it doesn’t provide any twisting force on the bolt. In this situation, you are only concerned with the component of force that is perpendicular to the displacement vector.

Question 3

Which of the following statements about these vectors is not correct?

Answer 3

To unscrew a bolt, a force in the direction parallel to the wrench must be applied. This force is a scalar with a magnitude B.