The scalars`la n dm` such that `l vec a+m vec b= vec c ,w h e r e vec a , vec ba n d vec c` are given vectors, are equal to

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q ,a n d vec r are parallel to vec a , vec b ,a n d vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to a. 1 b. 0 c. sqrt(3) d. 2

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0 then vec r is equal to

If vec a, vec b, vec c are three non-Coplanar nonzero vectors then (vec a * vec a) vec b xxvec c + (vec a * vec b) vec c xxvec a + (vec a * vec c) vec a xxvec ba is equal to

Given four vectors vec a, vec b, vec c, vec d such that vec a + vec b + vec c = alphavec d, vec b + vec c + vec d = betavec a and that vec a, vec a, vec b, vec c are non-coplanar, then the sum vec a + vec b + vec c + vec d is

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=odot

A parallelogram is constructed on 3 vec a+ vec ba n d vec a-4 vec b ,w h e r e| vec a|=6a n d| vec b|=8,a n d vec aa n d vec b are anti-parallel. Then the length of the longer diagonal is 40 b. 64 c. 32 d. 48

If vec a is a unit vector, vec a xxvec r = vec b, vec a * vec r = c, vec a * vec b = 0, then vec r is equal to

If vec a, vec b , vec c are three non- coplanar vectors such that vec a + vec b + vec c = alpha vec d and vec b +vec c + vec d = beta vec a, " then " vec a + vec b + vec c + vec d to equal to