Given
#veca=4vecp+vecq and vecb =vecp-vecq#
#absvecp=7 and absvecq=2#
#theta=<(vecp,vecq)=pi/4#
So
#absveca^2=16absvecp^2+absvecq^2+2xx4xxabsvecpabsvecqcostheta#
#=>absveca^2=16xx7^2+2^2+2xx4xx7xx2cos(pi/4)~~867.2#
Similarly
#absvecb^2=absvecp^2+absvecq^2-2absvecpabsvecqcostheta#
#=>absvecb^2=7^2+2^2-2xx7xx2cos(pi/4)~~33.2#
Let angle between #vec a and vec b# be #alpha#
Now #veca*vecb=4vecp*vecp-vecq*vecq-3vecp*vecq#
#=>veca*vecb=4absvecp^2-absvecq^2-3absvecp*absvecqcostheta#
#=>veca*vecb=4xx7^2-2^2-3xx7xx2xxcos(pi/4)~~162.3#
#cosalpha=(veca*vecb)/(absvecaabsvecb)=162.3/sqrt(867.2xx33.2)~~0.96#
So the length of the longer diagonal of a parallelogram built up on #veca and vecb#
#=sqrt(absveca^2+absvecb^2+2absvecaabsvecbcosalpha#
#=sqrt(867.2+33.2+2sqrt(867.2xx33.2)xx0.96)~~35#
So the length of the shorter diagonal of a parallelogram built up on #veca and vecb#
#=sqrt(absveca^2+absvecb^2+2absvecaabsvecbcos(pi-alpha)#
#=sqrt(867.2+33.2-2sqrt(867.2xx33.2)xx0.96)~~24#
