Prove that: `|(veca+vecb)xx(veca-vecb)|=2ab if veca_|_vecb`

Prove that: (2veca-vecb)xx (veca+2vecb)=5vecaxxvecb .

Prove that (veca+ vecb)*( veca+ vecb)=|veca|^2+| vecb|^2 , if and only if veca , vecb are perpendicular, given veca!= vec0, vecb!= vec0

Prove that (veca+3vecb)xx(veca+vecb)+(3veca-5vecb)xx(veca-vecb)=0

If veca, vecb, vecc and vecd ar distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.

If |veca+vecb|=|veca-vecb| show that veca_|_vecb .

Prove that : veca*(vecb+vec c)xx(veca+2vecb+3vec c)=[veca vecb vec c]

Prove that (vecaxxvecb)^(2)= |(veca.veca" "veca.vecb),(veca.vecb" "vecb.vecb)|

Prove that: (veca/a^2-vecb/b^2)^2=((veca-vecb)/(ab))^2

If veca and vecb are two vectors , then prove that (vecaxxvecb)^(2)=|{:(veca.veca" ",veca.vecb),(vecb.veca" ",vecb.vecb):}|

If veca and vecb are two vectors , then prove that (vecaxxvecb)^(2)=|{:(veca.veca" ",veca.vecb),(vecb.veca" ",vecb.vecb):}|