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The magnitude of the resultant of stack straight F subscript 1 with rightwards arrow on top space and space stack straight F subscript 2 with rightwards arrow on top is P; If direction of stack straight F subscript 2 with rightwards arrow on top is reversed, the resultant is Q.
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              space straight P squared plus straight Q squared space equals space 2 left parenthesis straight F subscript 1 squared plus straight F subscript 2 squared right parenthesis


Let straight theta be the  angle between two vectors space stack straight F subscript 1 with rightwards arrow on top space and space stack straight F subscript 2 with rightwards arrow on top.

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#6 {main}</pre>            ...(1)

If direction of stack straight F subscript 2 with rightwards arrow on top is reversed then, then angle between stack straight F subscript 1 with rightwards arrow on top space and space minus stack straight F subscript 2 with rightwards arrow on top becomes 180 degree minus straight theta.

∴           straight Q squared equals straight F subscript 1 squared plus straight F subscript 2 squared plus 2 straight F subscript 1 straight F subscript 2 cos left parenthesis 180 degree minus straight theta right parenthesis.

                 equals straight F subscript 1 squared plus straight F subscript 2 squared minus 2 straight F subscript 1 straight F subscript 2 cosθ       ...(2)

Adding (1) and (2), we get

              space straight P squared plus straight Q squared equals 2 left parenthesis straight F subscript 1 squared plus straight F subscript 2 squared right parenthesis

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