Resultant of two vectors `vecF_1 and vecF_2 is vecP` . When `vec_2` is reversed, the resultant is `vecQ` . Show that `(P^2+Q^2)=2(F_1^2+F_2^2)`

Explanation

When `vecF_2` is reversed it becomes `-vecF_2` .
From given conditions,
`vecF_1+vecF_2=vecP,vecF_1+(-vecF_2)=vecF_1-vecF_2=vecQ`
`therefore P^2+Q^2=(vecF_1+vec_2)^2+(vecF_1-vecF_2)^2`
=`F_1^2+F_2^2+2vecF_1*vecF_2+F_1^2+F_2^2-2vecF_1*vec_2`
`=2(F_1^2+F_2^2)`