Let ` vec r` be a unit vector satisfying ` vec rxx vec a= vec b ,w h e r e| vec a|=3a n d| vec b|=2.` Then ` vec r=2/3( vec a+ vec axx vec b)` b. ` vec r=1/3( vec a+ vec axx vec b` c. ` vec r=2/3( vec a- vec axx vec b` d. ` vec r=1/3(- vec a+ vec axx vec b`

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

If vec a+2 vec b+3 vec c=0,t h e n vec axx vec b+ vec bxx vec c+ vec cxx vec a= 2( vec axx vec b) b. 6( vec bxx vec c) c. 3( vec cxx vec a) d. vec0

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 aa n d vec b are two unit vectors that are mutually perpendicular. A unit vector that is equally inclined to vec a , vec ba n d vec axx vec b is a. 1/(sqrt(2))( vec a+ vec b+ vec axx vec b) b. 1/2( vec axx vec b+ vec a+ vec b) c. 1/(sqrt(3))( vec a+ vec b+ vec axx vec b) d. 1/3( vec a+ vec b+ vec axx vec b)

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d)dot (vec b- vec c)!=0,

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

Let vec r be a non-zero vector satisfying vec r . vec a= vec r . vec b= vec r . vec c=0 for given non-zero vectors vec a , vec ba n d vec cdot Statement 1: [ vec a- vec b vec b- vec c vec c- vec a]=0 Statement 2: [ vec a vec b vec c]=0

If vec a_|_ vec b , then vector vec v in terms of vec aa n d vec b satisfying the equation s vec v . vec a=0a n d vec v . vec b=1a n d[ vec v vec a vec b]=1 is a. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) b. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) c. vec b/(| vec b|^2)+( vec axx vec b)/(| vec axx vec b|^2) d. none of these

Let vec aa n d vec b be two non-zero perpendicular vectors. A vecrtor vec r satisfying the equation vec rxx vec b= vec a can be vec b-( vec axx vec b)/(| vec b|^2) b. 2 vec b-( vec axx vec b)/(| vec b|^2) c. | vec a| vec b-( vec axx vec b)/(| vec b|^2) d. | vec b| vec b-( vec axx vec b)/(| vec b|^2)