`|vecaxxhati|^2+|vecaxxhatj|^2+|vecaxxhatk|^2=` (A) `|veca|^2` (B) `2|veca|^2` (C) `3|veca|^2` (D) `4|veca|^2`

For any vector veca the value of (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2 is equal to (A) 4veca^2 (B) 2veca^2 (C) veca^2 (D) 3veca^2

If veca is any then |veca.hati|^2+|veca.hati|^2+|veca.hatk|^2= (A) |veca|^2 (B) |veca| (C) 2|vecalpha| (D) none of these

If veca is perpendicular to vecb then the vector vecaxx[vecaxx{vecaxx(vecaxxvecb)}] is equla (A) |veca|^2vecb (B) |veca|vecb (C) |veca|^3vecb (D) |veca|^4vecb

If veca is any vector and hati,hatj and hatk are unit vectors along the x,y and z directions then hatixx(vecaxxhati)+hatjxx(vecaxxhatj)+hatkxx(vecaxxveck)= (A) veca (B) -veca (C) 2veca (D) 0

If vecc=vecaxxvecb and vecb=veccxxveca then (A) veca.vecb=vecc^2 (B) vecc.veca.=vecb^2 (C) veca_|_vecb (D) veca||vecbxxvecc

For any vector veca |veca xx hati|^(2) + |veca xx hatj|^(2) + |veca xx hatk|^(2) is equal to

|veca pm vecb|^2 = |veca|^2 + |vecb|^2 pm 2|veca||vecb|cos theta and (veca + vecb).(veca - vecb) = |veca|^2 - |vecb|^2

If |vecaxxvecb|=2,|veca.vecb|=2 , then |veca|^(2)|vecb|^(2) is equal to

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: The value of sin(theta/2) is (A) 1/2 |veca-vecb| (B) 1/2|veca+vecb| (C) |veca-vecb| (D) |veca+vecb|

Let veca , vecb and vecc be three unit vectors such that |veca - vecb|^2 + |veca - vecc|^2 =8 . Then |veca + 2vecb|^2 + |veca + 2vecc|^2 is equal to ________.