find the magnitude and direction of the resultant of two vector. AndB in terms of their magnitudes and angle thera between them
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Answer:
Answer:Let OP and OQ represent the two vectors A and B making an angle. Then, using the parallelogram method of vector addition, OS represents the resultant vector R. <br> R= A+B <br> SN is normal to OP and OP and PM is normal to OS. <br> From the geometry of the figure. <br><br> but ON = OP + PN = A + Bcos<br> SN = B<br><br> or,.............(4.24a) <br> InOSN, SN= OS, and inPSN, SN= PS<br> Therefore,<br> or,................(4.24b) <br> Similarly, <br> PM= A<br> or............(4.24c)<br> Combining Eqs. we get, <br>................(4.24d) <br> Using Eqs, we get <br>...............(4.24 e)<br> Where R is given by Eq. <br> or...............(4.24f) <br> Eqs. (4.24a) givestjhe magnitude of the resultant and Eqs. (4.24e) and (4.24f) its direction. Equation (4.24a) is known as the law of cosines and Eq. (4.24d) as the law of sines.