The reflection of the point ` vec a` in the plane ` vec rdot vec n=q` is a. ` vec a+(( vec q- vec adot vec n))/(| vec n|)` b. ` vec a+2((( vec q- vec adot vec n))/(| vec n|)) vec n` c. ` vec a+(2( vec q+ vec adot vec n))/(| vec n|^2) vec n` d. none of these

The projection of point P( vec p) on the plane vec rdot vec n=q is ( vec s) , then a. vec s=((q- vec pdot vec n) vec n)/(| vec n|^2) b. vec s=p+((q- vec pdot vec n) vec n)/(| vec n|^2) c. vec s=p-(( vec pdot vec n) vec n)/(| vec n|^2) d. vec s=p-((q- vec pdot vec n) vec n)/(| vec n|^2)

Distance of point P( vec p) from the plane vec rdot vec n=0 is a. | vec pdot vec n| b. (| vec pxx vec n|)/(| vec n|) c. (| vec pdot vec n|)/(| vec n|) d. none of these

Line vec r= vec a+lambda vec b will not meet the plane vec rdot vec n=q , if a. vec bdot vec n=0, vec adot vec n=q b. vec bdot vec n!=0, vec adot vec n!=q c. vec bdot vec n=0, vec adot vec n!=q d. vec bdot vec n!=0, vec adot vec n=q

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

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

The orthogonal projection of vec a on vec b is (( vec adot vec b) vec a)/(|"a"|^2) b. (( vec adot vec b) vec b)/(| vec b|^2) c. vec a/(| vec a|) d. vec b/(| vec b|)

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

The intercept made by the plane vec rdot vec n=q on the x-axis is a. q/( hat idot vec n) b. ( hat idot vec n)/q c. ( hat idot vec n)/q d. q/(| vec n|)

If vec a=vec p+vec q,vec p xxvec b=0 and vec q*vec b=0 then prove that (vec b xx(vec a xxvec b))/(vec b*vec b)=vec q

Show that ( vec axx vec b)^2=| vec a|^2| vec b|^2-( vec adot vec b)^2=| [vec a.vec a, vec a.vec b],[ vec a.vec b, vec b.vec b]|