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

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)

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

Distance of the point P( vec p) from the line vec r= vec a+lambda vec b is a. |( vec a- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| b. |( vec b- vec p)+((( vec p- vec a)dot vec b) vec b)/(| vec b|^2)| c. |( vec a- vec p)+((( vec p- vec b)dot vec b) vec b)/(| vec b|^2)| 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|)

The equation of a line passing through the point vec a parallel to the plane vec r. 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

Given the following simultaneous equation for vectors vec xa n d vec y , vec x+ vec y= vec a , vec xxx vec y= vec b , vec xdot vec a=1,t h e n vec x= dot ( vec a+( vec axx vec b))/( vec a^2) (B) ( vec a+( vec axx vec b))/(| vec a|) (C) (( vec a+( vec axx vec b)))/( vec b^2) (D) none of these

Show that perpendicular distance of the point vec c from the line joining vec aa n d vec b is (| vec bxx vec c+ vec cxx vec a+ vec axx vec b)/(| vec b- vec a|)

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 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

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