Add the three vectors graphically to get the resultant vector. $\vec{V_1}$ $\vec{V_2}$ $\vec{V_3}$ $\vec{V_R} = \vec{V_1} + \vec{V_2} + \vec{V_3}$
Added by Xavier R.
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Step 1: Start by drawing the first vector, $\vec{V_1}$, from the origin. Show more…
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If several forces, each having different magnitudes and directions, act on a point object, their net effect can be represented by a single force called a resultant force. The magnitude and direction of the resultant force can be found using a special process known as vector addition. Vector addition can be done both analytically and graphically. In addition, resultant force vectors can be found experimentally. In the graphical technique of vector addition, each force is represented by an arrow whose length is proportional to the vector's magnitude. Each arrow is oriented at an angle θ that corresponds to the direction in which the force acts. In this technique, the tail of each arrow is connected to the head of the previous arrow until all forces have been drawn. A single arrow is then drawn from the tail of the first arrow (at the coordinate system origin) to the tip of the last arrow. This final arrow then represents the resultant force. Its length is proportional to the magnitude of the resultant vector and its angle θ corresponds to the direction in which the resultant force acts. The addition of two vectors A and B is shown in the diagram at the right. Using the "head-to-tail" method, we first draw vector A by placing its tail at the origin of the coordinate system. Next we draw vector B by placing its tail at the tip of vector A. The resultant vector R = A + B is found by drawing a straight line from the tail of vector A to the tip of vector B. The magnitude of R is proportional to its length and the direction in which it acts is the angle it makes with the horizontal. (Note: It doesn't matter which vector is drawn first. The result will be the same.)
Sri K.
$$ \vec{\mathbf{v}}_{1} \text { and } \vec{\mathbf{v}}_{2}, \text { add to a resultant } \vec{\mathbf{v}}=\vec{\mathbf{v}}_{1}+\vec{\mathbf{v}}_{2} $$ $$ \vec{\mathbf{V}}_{1} \text { and } \vec{\mathbf{V}}_{2} \text { if }(a) V=V_{1}+V_{2},(b) V^{2}=V_{1}^{2}+V_{2}^{2} $$ $$ (c) V_{1}+V_{2}=V_{1}-V_{2} $$
Graphical Method: Draw the resultant vector F3 = F1 + F2. Calculate the magnitude and the direction of the resultant vector force F3. Draw the vector -F2, give its magnitude and direction. Draw only the resultant vector force F4 = F1 - F2.
Paul G.
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