If ` vec a . vec b=betaa n d vec axx vec b= vec c ,t h e n vec b` is a.`((beta vec a- vec axx vec c))/(| vec a|^2)` b. `((beta vec a+ vec axx vec c))/(| vec a|^2)` c. `((beta vec c- vec axx vec c))/(| vec a|^2)` d. `((beta vec a+ vec axx vec c))/(| vec a|^2)`

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)

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

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

If vec a , vec b and vec c are three non-zero, non coplanar vector vec b_1= vec b-( vec bdot vec a)/(| vec a|^2) vec a , vec c_1= vec c-( vec cdot vec a)/(| vec a|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , , c_2= vec c-( vec cdot vec a)/(| vec a|^2) vec a-( vec bdot vec c)/(| vec b_1|^2) , b_1, vec c_3= vec c-( vec cdot vec a)/(| vec c|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1 , vec c_4= vec c-( vec cdot vec a)/(| vec c|^2) vec a=( vec bdot vec c)/(| vec b|^2) vec b_1 then the set of orthogonal vectors is ( vec a , vec b_1, vec c_3) b. ( vec a , vec b_1, vec c_2) c. ( vec a , vec b_1, vec c_1) d. ( vec a , vec b_2, vec c_2)

If vectors vec aa n d vec b are two adjacent sides of a parallelogram, then the vector respresenting the altitude of the parallelogram which is the perpendicular to a is vec b+( vec bxx vec a)/(| vec a|^2) b. ( vec a . vec b)/(| vec b|^2) c. vec b-( vec b . vec a)/(| vec a|^2) d. ( vec axx( vec bxx vec a))/(| vec b|^2)

If vec a= vec p+ vec q , vec pxx vec b=0a n d vec qdot vec b=0, then prove that ( vec bxx( vec axx vec b))/( vec bdot vec b)= vec qdot

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)

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

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

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