Final answer:
The dot product of (a x b) and b is zero because a x b is orthogonal to b, and the dot product of two orthogonal vectors is always zero.
Step-by-step explanation:
The question requires us to show that the dot product of the cross product of two vectors a and b with vector b is zero. The cross product a x b results in a vector that is orthogonal (perpendicular) to both a and b. Since this new vector is perpendicular to b, their dot product will be zero.
By the properties of scalar products of orthogonal unit vectors in the Cartesian coordinate system, we know that the dot product of two orthogonal vectors is zero because the cosine of 90° is zero. Specifically, when we have (a x b) · b, the cross product a x b is a vector that is orthogonal to vector b, and hence their dot product will be zero.