5. (a) By using the Right-Hand Rule, determine the direction of vector $\vec{C}$. i) $\bar{A} \times \vec{B}=\bar{C}$ ii) $\vec{B} \times \vec{A}=\vec{C}$
Solution
Step 1 ：The Right-Hand Rule is a method used to determine the direction of the cross product in vector multiplication. For \(\vec{A} \times \vec{B}=\vec{C}\), if you point your index finger in the direction of \(\vec{A}\) and your middle finger in the direction of \(\vec{B}\), your thumb will point in the direction of \(\vec{C}\).
Step 2 ：For \(\vec{B} \times \vec{A}=\vec{C}\), if you point your index finger in the direction of \(\vec{B}\) and your middle finger in the direction of \(\vec{A}\), your thumb will point in the direction of \(\vec{C}\).
Step 3 ：Final Answer: For \(\vec{A} \times \vec{B}=\vec{C}\), the direction of \(\vec{C}\) is the direction your thumb is pointing when your index finger is pointing in the direction of \(\vec{A}\) and your middle finger is pointing in the direction of \(\vec{B}\).
Step 4 ：For \(\vec{B} \times \vec{A}=\vec{C}\), the direction of \(\vec{C}\) is the direction your thumb is pointing when your index finger is pointing in the direction of \(\vec{B}\) and your middle finger is pointing in the direction of \(\vec{A}\).
