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 r. vec n=q is ( vec s) , then a. vec s=((q- vec p. vec n) vec n)/(| vec n|^2) b. vec s=p+((q- vec p. vec n) vec n)/(| vec n|^2) c. vec s=p-(( vec p. vec n) vec n)/(| vec n|^2) d. vec s=p-((q- vec p. 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|^2)) 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 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

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

Let vec pa n d vec q be any two orthogonal vectors of equal magnitude 4 each. Let vec a , vec b ,a n d vec c be any three vectors of lengths 7sqrt(15)a n d2sqrt(33), mutually perpendicular to each other. Then find the distance of the vector ( vec adot vec p) vec p+( vec adot vec q) vec q+( vec adot( vec pxx vec q))( vec pxx vec q)+( vec bdot vec p) vec p( vec bdot vec q) vec q+( vec bdot( vec pxx vec q))( vec pxx vec q)+( vec cdot vec p) vec p+( vec cdot vec q) vec q+( vec cdot( vec pxx vec q))( vec pxx vec q) from the origin.

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 a. 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 x+ vec cxx vec y= vec aa n d vec y+ vec cxx vec x= vec b ,w h e r e vec c is a nonzero vector, then which of the following is not correct? a. vec x=( vec bxx vec c+ vec a+( vec c dot vec a) vec c)/(1+ vec c dot vec c) b. vec x=( vec cxx vec b+ vec b+( vec c dot vec a) vec c)/(1+ vec c dot vec c) c. vec y=( vec axx vec c+ vec b+( vec c dot vec b) vec c)/(1+ vec c dot vec c) d. none of these