Lagrange identity: If two vector `veca; vecb` are any two vectors `|vecaxx vecb|^2 =( |veca|^2 |vecb|^2 - (veca . vecb)^2)`

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

If veca and vecb are non - zero vectors such that |veca + vecb| = |veca - 2vecb| then

For any two vectors veca and vecb prove that |veca.vecb|lt+|veca||vecb|

For any two vectors veca and vecb prove that |veca+vecb|lt+|veca|+|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)

If veca and vecb are two vectors, such that |veca xx vecb|=2 , then find the value of [veca vecb veca xx vecb]

If veca and vecb are two vectors, such that |veca xx vecb|=2 , then find the value of [veca vecb veca xx vecb]

If veca, vecb are unit vectors such that |veca +vecb|=1 and |veca -vecb|=sqrt3 , " then " |3veca +2vecb|=

For any two vectors veca and vecb write when | veca + vecb|= | veca-vecb| holds.