If `|vec A|=10`, `|vec B|=2`, and `vec A . vec B = 12`, `|vec A xx vec B|` =_____.

Given |vec a|=10,|vec b|=2 and vec avec b=12, find |vec a xxvec b|

If | vec A| = 2, | vec B| =5 and | vec A xx vec B | =8 , din the value of (vec A. vec B0 .

If three vectors vec A, vec B and vec C are such that vec A .vec B =vec A .vec C , vec A xx vec B = vec A xx vec C , vec A!= vec 0 then prove that vec B =vec C .

If? B, c are three vectors such that | vec a | = 5, | vec b | = 12 and | vec c | = 13 and vec a + vec b + vec c = 0 then vec a * vec b + vec b * vec c + vec c * vec a

For any to vectors vec A and vec B , prove that |vec A xx vec B|^2 = A^2 B^2 - ( vec A. vec B)^2 .

If vec A, vec B and vec C are vectors such that | vec B | - | vec C | * Prove [(vec A + vec B) xx (vec A + vec C)] xx (vec B + vec C) * (case B + case C) = 0

If vec A and vec B are two vectors satisfying the relation vec A cdot vec B = |vec A xx vec B| . Then the value of |vec A - vec B| will be :

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

36. If vec a, vec b, vec c and vec d are unit vectors such that (vec a xx vec b) .vec c xx vec d = 1 and vec a.vec c = 1/2 then a) vec a, vec b and vec c are non-coplanar b) vec b, vec c, vec d are non -coplanar c) vec b, vecd are non parallel d) vec a, vec d are parallel and vec b, vec c are parallel

Fven that vec A xx vec B= vec B xx vec C = vec 0 . If vec A. vec B and vec C are not null vectors, find the value of vec Cxx vec A .