Answer:
The first two statements are false
The third statement is true
Explanation:
<u>The dot product assures that the integrand is always nonnegative.</u>
The dot product may be negative, this could ocurr when the vectors are directed oposite each other, for example take the unitary vector i and -i its doct product will give -1.
Another way to consider this is to take the definition of the dot product in terms of teh angle between the vetcors:
When θ>π :
cos(θ)<0
<u>The dot product indicates that only the component of the force perpendicular to the path contributes to the integral</u>
In fact the dot product is a projection of the vectors, the perpendicular component may be obtained using the cross product
<u>The dot product indicates that only the component of the force parallel to the path contributes to the integral.</u>
This one is true, since the dot product gives the projection of one vector to another, that is, the parallel component of the vector among the other one