Question #2970f

1 Answer
Jul 26, 2015

Answer:

Force is a vector. Let me illustrate it's use in the following section.

Explanation:

Here is how that Newton's second law appeared in nineteenth century notation,

#F""_x = ma""_x#
#F""_y = ma""_y#
#F""_z = ma""_z#

But, with using vector notation, the equation simply becomes

# vecF = mveca#
Where, # vecF = F""_xveci + F""_yvecj + F""_zveck# , is the force in vector notation.
Acceleration might also be represented similarly.

The three equations are combined to one : a great economy for the three we would need otherwise.

Now, let us consider work done by a force #vecF# acting at angle #theta# displacing an object through #vecR#.

The work done, is given as #W = FR Cos theta#.
In terms of scalar product, it becomes,

#W = vecF*vecR#

Similarly, if a force #vecF# acts on an object to rotate it at an angle #theta# with #vecR#, the axis of rotation, the torque is given as,

# tau = FR Sin theta#

In vector notation and incorporating a direction for the torque, the expression looks like

#vectau = vecR X vecF#.

There are several other vectors which are related to physical problems. EM fields, gravitational fields, force, displacement, acceleration, momentum, torque, all are vectors, just to name a few.