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
Answer: The magnitude of the net magnetic field (in microTesla) at point P is 0.287.
The direction of the net magnetic field at point P is pointing into the page.
Explanation: Please see the attachments below
#6). The tangent of an angle in a right triangle is
(opposite side) / (adjacent side) .
The side opposite the marked angle is 4cm.
The side adjacent to the marked angle is 12cm.
The tangent of the marked angle is (4cm / 12cm) = 1/3 .
The marked angle is the angle whose tangent is 1/3 .
You can find that online, or with your calculator, slide rule, Curta, or book.
#7). The cosine of an angle in a right triangle is
(adjacent side) / (hypotenuse) .
The side adjacent to the marked angle is 15m.
The hypotenuse is 19m.
The cosine of the marked angle is (15m / 19m) = about 0.78947...
The marked angle is the angle whose cosine is 0.78947... .
You can find that online, or with your calculator, slide rule, Curta, or book.