Final answer:
The dot product is used to find angles and scalar quantities, while the cross product is used to find vector quantities and describe rotations.
Step-by-step explanation:
The dot product and the cross product are two different mathematical operations used in vector algebra. The dot product, also known as the scalar product, results in a scalar, while the cross product, also known as the vector product, results in a vector.
The dot product is used to find angles between vectors and in the definitions of derived scalar physical quantities such as work or energy. The cross product is used in the definitions of derived vector physical quantities such as torque or magnetic force, and in describing rotations.
When choosing between dot product and cross product, it depends on the specific problem and the type of information you need to find. If you want to find a scalar quantity like work or angle, use the dot product. If you want to find a vector quantity like torque or rotational force, use the cross product.