Triangle Law And Polygon Law
Triangular law of vector addition
Statement - 1: If two vectors are represented both in magnitude and direction as the adjacent sides of a triangle taken in order, then the closing side taken in reverse order represents the resultant both in magnitude and direction.
Let the two vector \(\vec A\) and \(\vec B\), inclined at an angle q be acting on a particle at the same time. Let they be represented in magnitude and direction by two sides \(\vec OP\) and \(\vec PQ\) of triangle OPQ, taken in the same order.
Then, according to triangle law of vector addition, the resultant \(\vec R\) is represented by the third side \(\vec OQ\) of triangle, taken in opposite order.
Statement - 2: If three vectors are such that their resultant is zero vector or null vector then they can be represented both in magnitude and direction as the adjacent sides of a triangle taken in order.
Let \(
\overline A ,\overline B ,\overline C
\)are acting at a point such that \(
\overline A + \overline B + \overline C = \overline 0
\) as shown in figure
If the resultant of three vectors is a null vector, then they can be represented both in direction and magnitude as the adjacent sides of a triangle taken in order \(
\overline a + \overline b + \overline c = \overline 0
\)
Note: A zero vector or null vector has no magnitude and possesses inderterminate (undefined) direction