Thread: one more vector problem

The quiz is as under:

two forces whose magnitudes are in the ratio 3:7 give a resultant of 3 sq.root of 79 N. If the angle of inclination be 60 degrees, find the magnitude of each force.

F1 be 3x and F2 be 7x. Resultant F is sq.root of 79. Since the inclination is 60 degree, I take the angle as 30 degrees. One side of the triangle is 3x, second one is 7x and third one is 3 sq.root 79 and one of the angles of the triangle is 30 degrees.

Whether my assumptions are correct and if so, how to go about?

Kindly guide me.

Thanks in advance.

Hello, arangu1508!

. No!

You assumed that the diagonals of a parallelogram bisect the vertex angles.
. . This is not true . . .

We have this parallelogram:

Code:

                    7x
            *  *  *  *  *  *  *
           *                 *
          *                 *
      3x *                 * 3x
        *                 *
       * 60          120 *
      *  *  *  *  *  *  *
              7x

which gives us this triangle:

Code:

                              *
                          *  *
               __     *     *
             3√79 *        * 3x
              *           *
          *          120 *
      *  *  *  *  *  *  *
               7x

Now we can use the Law of Cosines:
. .

Got it?

Mr. Soroban,

Thank you. I got it.

with regards,

Aranga