Question

Question #2970f

Answer 1

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.