State true or false: If `|veca+vecb|=|veca-vecb|`, then the vectors `vecaandvecb` are orthogonal

State true or false: If |veca|=|vecb| , then necessarily it implies veca=+-vecb .

If |veca+vecb|=|veca-vecb|, (veca,vecb!=vec0) show that the vectors veca and vecb are perpendicular to each other.

State true or false: If vecaandvecb are adjacent sides of a rhombus, then veca.vecb=0 .

If veca" and "vecb are any two vectors such |veca+vecb|=|veca-vecb| find the angle between veca" and "vecb

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|

If veca,vecb are two unit vectors such that |veca + vecb| = 2sqrt3 and |veca -vecb|=6 then the angle between veca and vecb , is

Let veca=hati+2hatj and vecb=2hati+hatj. Is |veca|=|vecb| Are the vectors veca and vecb equal?.

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

Given that veca and vecb are unit vectors. If the vectors vecp=3veca-5vecb and vecq=veca+vecb are mutually perpendicular, then

If veca, vecb, vecc are vectors such that veca.vecb=0 and veca + vecb = vecc then: