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

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ,a n d vec c are nonzero vectors, then 1. vec a , vec b ,a n d vec c can be coplanar 2. vec a , vec b ,a n d vec c must be coplanar 3. vec a , vec b ,a n d vec c cannot be coplanar 4.none of these

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 ba n d vec c are two-noncollinear vectors such that vec a||( vec bxx vec c), then prove that ( vec axx vec b) . ( vec axx vec c) is equal to | vec a|^2( vec bdot vec c)dot

If vec rdot vec a= vec rdot vec b= vec rdot vec c=0,w h e r e vec a , vec b ,a n d vec c are non-coplanar, then a. vec r_|_( vec cxx vec a) b. vec r_|_( vec axx vec b) c. vec r_|_( vec bxx vec c) d. vec r= vec0

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

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, 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

Let vec r=( vec axx vec b)sinx+( vec bxx vec c)cosy+2( vec cxx vec a),w h e r e vec a , vec ba n d vec c are there non-coplanar vectors. It is given that vec r is perpendicular to vec a+ vec b+ vec c , the minimum value of x^2+y^2 is equal to (A) pi^2 (B) (pi^2)/4 (C) (5pi^2)/4 (D) none of these