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 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

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|=0

vec aa n d vec b are two non-collinear unit vector, and vec u= vec a-( vec adot vec b) vec ba n d vec v= vec axx vec bdot Then | vec v| is | vec u| b. | vec u|+| vec udot vec b| c. | vec u|+| vec udot vec a| d. none of these

The equation of a line passing through the point vec a parallel to the plane vec rdot vec n=q and perpendicular to the line vec r= vec b+t vec c is a. vec r= vec a+lambda( vec nxx vec c) b. ( vec r- vec a)xx( vec nxx vec c) c. vec r= vec b+lambda( vec nxx vec c) d. none of these

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 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 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| .