Indicate which of the following statements about vector algebra and vector functions are true:
1. The sum of vectors is commutative, associative, has a neutral element (null vector), and an opposite vector.
2. The derivative of a scalar product of two vectors is equal to the scalar product of the derivative of the first vector by the second vector plus the scalar product of the first vector by the derivative of the second vector.
3. The derivative of a sum of vectors is equal to the sum of the derivatives of the vectors.
4. The derivative of a vector function of a scalar variable is a new vector whose components are the derivatives of the components of the vector function.
5. The product of a scalar by a vector has the properties of distributivity with respect to vectors, associativity with respect to scalars, and the existence of a neutral scalar.
6. The derivative of a vector product of two vectors, both functions of the same scalar variable, is equal to the derivative of the first vector multiplied vectorially by the second vector plus the derivative of the second vector multiplied vectorially by the first vector.
true
true
true
true
true
true
a) 1, 2, and 3 are true.
b) 2, 3, and 4 are true.
c) 3, 4, and 5 are true.
d) 4, 5, and 6 are true.