If `( vec axx vec b)^2+( vec adot vec b)^2=144a n d| vec a|=4,` then find the value of `| vec b|dot`

If | vec axx vec b|^2=( vec adot vec b)^2=144\ a n d\ | vec a|=4 , find vec bdot

if (vec axvec b) ^ (2) + (vec a * vec b) ^ (2) = 144, | vec a | = 4 then | vec b | =

If |vec a|=2|vec b|=5 and |vec a xxvec b|=8, then find the value of vec a.vec b.

If vec rdot vec a=0, vec rdot vec b=1a n d[ vec r vec a vec b]=1, vec adot vec b!=0,( vec adot vec b)^2-=| vec a|^2| vec b|^2=1, then find vec r in terms of vec aa n d vec bdot

If vec a, vec b and vec c are perpendicular to vec b + vec c, vec c + vec a, vec a + vec b respectively and if | vec a + vec b | = 6, | vec b + vec c | = 8 and | vec c + vec a | = 10 then find the value of vec a + vec b + vec c

(vec a-vec b) * (vec a + vec b) = 27 and | vec a | = 2 | vec b | find | vec a | and | vec b |

If two vectors vec a and vec b are such that |vec a|=2,|vec b|=1 and vec avec b=1, then find rthe value of (3vec a-5vec b)2vec a+7vec b

Let vec a , vec b , vec c are three vectors , such that vec a + vec b + vec c = vec 0 .If , |vec a|=3 , |vec b|=4 and | vec c|=5 , then the value of, |vec a+vec b|^(2) + |vec b-vec c|^(2) + |vec c+vec a|^(2) , equal to :

If vec aa n d vec b are two vectors and angle between them is theta, then | vec axx vec b|^2+( vec adot vec b)^2=| vec a|^2| vec b|^2 | vec axx vec b|=( vec adot vec b),iftheta=pi//4 vec axx vec b=( vec adot vec b) hat n ,(w h e r e hat n is unit vector,) if theta=pi//4 ( vec axx vec b)dot( vec a+ vec b)=0

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3