Final answer:
The scalar product of vectors r and F is rx*Fx + ry*Fy, which is a dot product. The vector product in two dimensions is zero as there is no third component.
Step-by-step explanation:
Scalar and Vector Products of Two Vectors
To answer the question regarding the scalar and vector products of the vectors r and F given by r= rxi + ryj and F = Fxi + Fyj, we need to calculate the dot product (scalar product) and the cross product (vector product).
The scalar product of r and F is calculated by multiplying their corresponding components and then adding those products:
Scalar product of r and F = (rxi + ryj) · (Fxi + Fyj) = rx*Fx + ry*Fy
The vector product is obtained by taking the product of the magnitudes of the two vectors and the sine of the angle between them, directed perpendicular to the plane defined by the vectors. In two dimensions, since there is no k component, the vector product in this case is zero.
Physical quantities that arise from scalar and vector products include work and torque, respectively. Work is the scalar product of force and displacement, whereas torque is the vector product of the position vector and the force applied.