10 True or false questions of vector addition and subtractiomln

Here are 10 true or false questions about vector addition and subtraction:

1. Vector addition is commutative, meaning $\vec{A} + \vec{B} = \vec{B} + \vec{A}$.
2. The magnitude of the sum of two vectors is always equal to the sum of their magnitudes, i.e., $|\vec{A} + \vec{B}| = |\vec{A}| + |\vec{B}|$.
3. Subtracting vector $\vec{B}$ from vector $\vec{A}$ is equivalent to adding the negative of vector $\vec{B}$ to vector $\vec{A}$, i.e., $\vec{A} - \vec{B} = \vec{A} + (-\vec{B})$.
4. If two non-zero vectors are perpendicular, their sum will always have a magnitude greater than either individual vector's magnitude.
5. The resultant vector of $\vec{A} + \vec{B}$ always points in the direction of the vector with the larger magnitude.
6. Adding the zero vector to any vector does not change the vector, i.e., $\vec{A} + \vec{0} = \vec{A}$.
7. If $\vec{A} + \vec{B} = \vec{0}$, then $\vec{A}$ and $\vec{B}$ must have the same magnitude and point in opposite directions.
8. Vector addition follows the associative law: $(\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C})$.
9. When adding vectors graphically using the head-to-tail method, the resultant vector is drawn from the tail of the first vector to the head of the last vector.
10. If two vectors have the same magnitude, their difference will always be the zero vector.