If `l ,\ m ,\ n` are scalars and ` vec a ,\ vec b ,\ vec c` are vectors, prove that `|l vec a+m vec b+n vec c|^2=l^2| vec a|^2+m^2|| vec b|^2+n^2| vec c|^2+2\ {l m( vec adot vec b)+m n( vec bdot vec c)+n l( vec cdot vec a)}` . Also deduce that `|l vec a+m vec b+n vec c|^2=l^2 vec|a|^2+m^2| vec b|^2+n^2| vec c|^2if\ vec a ,\ vec b ,\ vec c` are mutually perpendicular vectors.