Final answer:
The expressions in question involve correct use of vector operations. For scalar fields and magnetic forces, understanding vector properties is key. The magnetic force on a particle in a field depends on the right-hand rule for cross products.
Step-by-step explanation:
The student appears to be asking about vector operations, specifically about what might be wrong with certain expressions involving vectors (Part 21) and about the resultant force on a charged particle in a magnetic field (Part 41). For Part 21, the expressions given involve vector and scalar multiplications, and for each, the student must identify if the operation is meaningful given vector properties. For Part 41, the question involves the cross product of vectors, specifically the magnetic force on a charged particle moving in a magnetic field. The correct answers depend on understanding vector multiplication rules and the right-hand rule for magnetic force.
Regarding Part 21 (a), the expression C = Ả · B implies the dot product, which correctly results in a scalar. For (c), C = Ả × B signifies the cross product, which correctly results in a vector. However, if the student's original (c) lacked the vector notation over 'C' indicating that 'C' is a vector, it would be incorrect as the dot product of two vectors is a scalar, not a vector.
For Part 41, to determine the magnetic force on an alpha particle (a charged particle), use Fleming's left-hand rule or the cross product between the velocity vector of the particle and the magnetic field direction. For (a), if the particle moves in the positive x-direction and the magnetic field is parallel to the z-axis, the magnetic force would be in the negative y-direction due to the right-hand rule (since the alpha particle is positively charged). For (c), there would be no magnetic force since the particle is moving parallel to the field lines. The force on a charged particle in a magnetic field is given by the Lorentz force law, which includes the cross product of the velocity and magnetic field vectors.