Let `vec a, vec b` and `vec c` be the three vectors such that `|veca| = 3 , |vec b| = 4, |vec c| = 5`, and each one of them being perpendicular to the sum of the other two . Find `|vec a + vec b + vec c|`.

If vec a and vec b are two non- zero vectors such that | vec a + vec b| = |vec a - vec b| , then show that vec a and vec b are perpendicular.

The vectors vec a and vecb are such that |vec a| = 2, |vec b| = 3, veca.vecb = 4 .Find |veca - vec b|

If vec a, vec b, vec c are three given vectors show that [ vec a + vecb + vec c , vecb + vec c , vec a + vec b + vec c ]=0.

If veca = vec b+ vec c , then is it true that |veca| = |vec b| + |vec c| ? Justify your answer.

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of vec a+ vec b+ vec c

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

If vec a , vec b ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].

Let vec a , vec ba n d vec c be three units vectors such that 2 vec a+4 vec b+5 vec c=0. Then which of the following statement is true? a. vec a is parallel to vec b b. vec a is perpendicular to vec b c. vec a is neither parallel nor perpendicular to vec b d. none of these

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .