Law of triangle of vector addition:
Suppose there are two vectors \(\vec{A}\) and \(\vec{B}\) making an angle θ with each other Addition method of these two vectors is given below.
Method:
1. First of all we draw a basic oa of length equal to magnitude of one vector along its direction.
2. Now we draw a line from final point of oa i.e., from a making an angle (180 - θ) with oa.
3. We cut an arc of length equal to magnitude of other vector. It represents vector \(\vec{B}\) with terminus as b.
4. Now initial point of \(\vec{A}\) and terminus of \(\vec B\) is joined which provides the resultant \(\vec R\) of \(\vec A\) and \(\vec B\). By measuring the length of \(\vec R\). We get the magnitude of resultant. This whole process is shown in.
Addition of vector obeys commutative law:
if \(\vec A\) and \(\vec B\) are two vector quantities, then
\(\vec A + \vec B = \vec B + \vec A\)
Suppose oa = \(\vec A\) and ab = \(\vec B\), from law of triangle of vector addition for ∆oab
or \(o\vec b = o\vec a + a\vec b\)
or \(\vec R = \vec B + \vec A\ ....(1)\)
On applying the same law of ∆acb
\(\vec ob = \overrightarrow{oc} + \vec cb\)
or \(\vec R = \vec B + \vec A\ ...(2)\)
On comparing equations (1) and (2), we have
\(\vec A + \vec B = \vec B + \vec A\)
