# Question #2970f

Jul 26, 2015

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,

$F {\text{_x = ma}}_{x}$
$F {\text{_y = ma}}_{y}$
$F {\text{_z = ma}}_{z}$

But, with using vector notation, the equation simply becomes

$\vec{F} = m \vec{a}$
Where, $\vec{F} = F {\text{_xveci + F""_yvecj + F}}_{z} \vec{k}$ , 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 $\vec{F}$ acting at angle $\theta$ displacing an object through $\vec{R}$.

The work done, is given as $W = F R C o s \theta$.
In terms of scalar product, it becomes,

$W = \vec{F} \cdot \vec{R}$

Similarly, if a force $\vec{F}$ acts on an object to rotate it at an angle $\theta$ with $\vec{R}$, the axis of rotation, the torque is given as,

$\tau = F R S \in \theta$

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

$\vec{\tau} = \vec{R} X \vec{F}$.

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.