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=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)

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

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

If vec a , vec ba n d vec c are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is a. vec a+ vec b+ vec c b. vec a/(| vec a|)+ vec b/(| vec b|)+ vec c/(| vec c|) c. vec a/(| vec a|^2)+ vec b/(| vec b|^2)+ vec c/(| vec c|^2) d. | vec a| vec a-| vec b| vec b+| vec c| vec c

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+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

If axx(bxxc)=(axxb)xxc , then ( vec cxx vec a)xx vec b= vec0 b. vec cxx( vec axx vec b)= vec0 c. vec bxx( vec cxx vec a) vec0 d. ( vec cxx vec a)xx vec b= vec bxx( vec cxx vec a)= 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

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 non-zero vectors vec aa n d vec b are equally inclined to coplanar vector vec c ,t h e n vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b