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

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

Show that, (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) .

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

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):}|

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

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)