Non-zero vectors `vec a, vec b and vec c` satisfy `vec a. vec b =0,(vec b-vec a)(vec b +vec c)=0 and 2|vec b + vec c|=|vec b-vec a|.` If `vec a=mu vec b+4vec c` then possible value of `mu` are

Prove that if the vectors vec a, vec b, vec c satisfy vec a+ vec b + vec c = vec 0 , then vec bxx vec c = vec c xx vec a = vec a xx vec b

For any three vectors vec a, vec b , vec c , show that vec a xx (vec b + vec c) + vec b xx (vec c + vec a) + vec c xx (vec a + vec b) = 0

For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot vec c|=| vec a|| vec b|| vec c| holds if and only if a. vec a* vec b=0, vec b* vec c=0 b. vec b* vec c=0, vec c* vec a=0 c. vec c* vec a=0, vec a* vec b=0 d. vec a* vec b=0, vec b* vec c=0, vec c* vec a=0

For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot vec c|=| vec a|| vec b|| vec c| holds if and only if a. vec a* vec b=0, vec b* vec c=0 b. vec b* vec c=0, vec c* vec a=0 c. vec c* vec a=0, vec a* vec b=0 d. vec a* vec b=0, vec b* vec c=0, vec c* vec a=0

For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot vec c|=| vec a|| vec b|| vec c| holds if and only if a. vec a* vec b=0, vec b* vec c=0 b. vec b* vec c=0, vec c* vec a=0 c. vec c* vec a=0, vec a* vec b=0 d. vec a* vec b=0, vec b* vec c=0, vec c* vec a=0

For non-zero vectors vec a , vec b ,a n d vec c ,|( vec axx vec b)dot vec c|=| vec a|| vec b|| vec c| holds if and only if a. vec a* vec b=0, vec b* vec c=0 b. vec b* vec c=0, vec c* vec a=0 c. vec c* vec a=0, vec a* vec b=0 d. vec a* vec b=0, vec b* vec c=0, vec c* vec a=0

Three vectors vec a, vec b and vec c satisfy the condition vec a + vec b + vec b + vec c = vec 0 .Evaluate the quantity mu = vec a * vec b + vec b * vec c + vec c * vec a , if | vec a | = 1 | vec b | = 4 and | vec c | = 2

If vec a, vec b and vec c are non coplaner vectors such that vec b xxvec c = vec a, vec c xxvec a = vec b and vec a xxvec b = vec c then | vec a + vec b + vec c | =

If vec a is a non-zero vector and vec a * vec b = vec a * vec c, vec a xxvec b = vec a xxvec c, then

If vec a, vec b , and vec c are vectors such that |vec b| = |vec c| , then {[(vec a + vec b) xx (vec a + vec c)] xx (vec b xx vec c)} . (vec b + vec c) =