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

Prove that (vecaxxvecb)^2=veca^2b^2-(veca.vecb)^2 .

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

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

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

Prove that |veca xx vecb|^(2)=|{:(veca*veca,veca *vecb),(veca*vecb,vecb*vecb):}| .

IF veca and vecb re two vectors show that (vecaxxvecb)^2=a^2b^2-(veca.vecb)^2

If veca and vecb are any two vectors , then prove that |vecaxxvecb|^(2)=|veca|^(2)|vecb|^(2)-(veca.vecb)^(2)=|{:(veca.veca,veca.vecb),(veca.vecb,vecb.vecb):}| or |vecaxxvecb|^(2)+(veca.vecb)^(2)=|veca|^(2)|vecb|^(2) (This is also known as Lagrange identily)

If veca and vecb be two non collinear vectors such that veca=vecc+vecd , where vecc is parallel to vecb and vecd is perpendicular to vecb obtain expression for vecc and vecd in terms of veca and vecb as: vecd= veca- ((veca.vecb)vecb)/b^2,vecc= ((veca.vecb)vecb)/b^2

[(veca,vecb,axxvecb)]+(veca.vecb)^(2)=

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