Evaluate :
`vec a . vec a`
( A )   0
( B )   1
( C )   `| vec a |^2`
( D )   `| vec a |`

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

Let | vec a | = | vec b | = 2 and | vec c | = 1 Also (vec a-vec c) * (vec b-vec c) = 0 and | vec a-vec b | ^ (2) + | vec a + vec b | = 16 then | vec a-vec b | ^ (2) + 2vec c * (vec a + vec b) has the value equal to

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 = muvec b + 4vec c then possible value of mu are

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

If vec r=x_1( vec axx vec b)+x_2( vec bxx vec a)+x_3( vec cxx vec d) and 4[ vec a vec b vec c]=1, then x_1+x_2+x_3 is equal to (A) 1/2 vecr .( vec a+ vec b+ vec c) (B) 1/4 vecr.( vec a+ vec b+ vec c) (C) 2 vecr.( vec a+ vec b+ vec c) (D) 4 vecr.( vec a+ vec b+ vec c)

A B C D E is pentagon, prove that vec A B + vec B C + vec C D + vec D E+ vec E A = vec0 vec A B+ vec A E+ vec B C+ vec D C+ vec E D+ vec A C=3 vec A C

Let vec a, vec b, vec c, vec d be unit vectors such that vec a * vec b + vec a * vec c + vec a * vec d + vec b * vec c + vec b * vec d + vec c * vec d = -2 Then [vec with bvec c] + [vec with bvec d] + [vec with cvec d] + [vec bvec cvec d] =

Three vectors vec a , vec b , vec c satisfy the condition vec a+ vec b+ vec c= vec0 . Evaluate the quantity mu= vec adot vec b+ vec bdot vec c+ vec cdot vec a , if | vec a|=1, | vec b|=4 a n d | vec c|=2.

If vec a = vec b + vec c, vec b xxvec d = vec 0, vec c * vec d = 0 then (vec d xx (vec a xxvec d)) / (| vec d | ^ (2)) is always equal to

If (vec a-vec b) * (vec a + vec b) = 0, then (a) vec a and vec b are perpendicular (b) vec a and vec b are parallel (c) | vec a | = | vec b | (d) vec a = 2vec b