Now, consider whether the following statements are true or false:
a) the dot product assures that the integrand is always non-negative.
b) the dot product indicates that only the component of the force perpendicular to the path contributes to the integral.
c) the dot product indicates that only the component of the force parallel to the path contributes to the integral.
enter t for true or f for false for each statement. separate your responses with commas.

A)F

B)F

C)T

Explanation:

A)

This is not always true that the product of the two vector's always non-negative .It may be positive or negative.

That is why this statement is false.

B)

The unit vectors in three perpendicular direction is i ,j and k.

We know that for unit vectors

i.i=j.j=k.k= 1

i .j= j.k=k.i=0

Therefore only  parallel component of the force will contribute in the integral part instead of perpendicular component of the force.

That is why this statement is false.

C)

This statement is True.

A)F

B)F

C)T