The projection of point `P( vec p)` on the plane ` vec rdot vec n=qi s( 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 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

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

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

Let ABCD be a parallelogram such that vec A B= vec q , vec A D= vec p""a n d""/_B A D be an acute angle. If vec r is the vector that coincides with the altitude directed from the vertex B to the side AD, then vec r is given by (1) vec r=3 vec q-(3( vec pdot vec q))/(( vec pdot vec p)) vec p (2) vec r=- vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p (3) vec r= vec q+(( vec pdot vec q)/( vec pdot vec p)) vec p (4) vec r=-3 vec q+(3( vec pdot vec q))/(( vec pdot vec p)) vec p

Find the equation of a straight line in the plane vec r* vec n=d which is parallel to vec r= vec a+lambda vec b and passes through the foot of the perpendicular drawn from point P( vec a)to vec rdot vec n=d(w h e r e vec ndot vec b=0)dot a. vec r= vec a+((d- vec a*vec n)/(n^2))n+lambda vec b b. vec r= vec a+((d- vec a* vec n)/n)n+lambda vec b c. vec r= vec a+(( vec a* vec n-d)/(n^2))n+lambda vec b d. vec r= vec a+(( vec a* vec n-d)/n)n+lambda vec b

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 a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec adot vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec bdot vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec cdot vec d)/([ vec a vec b vec c])( vec axx vec b)

Vectors vec Aa n d vec B satisfying the vector equation vec A+ vec B= vec a , vec Axx vec B= vec ba n d vec A*vec a=1,w h e r e vec aa n d vec b are given vectors, are a. vec A=(( vec axx vec b)- vec a)/(a^2) b. vec B=(( vec bxx vec a)+ vec a(a^2-1))/(a^2) c. vec A=(( vec axx vec b)+ vec a)/(a^2) d. vec B=(( vec bxx vec a)- vec a(a^2-1))/(a^2)

Prove that if [ vec l vec m vec n] are three non-coplanar vectors, then [ vec l vec m vec n]( vec axx vec b)=| vec ldot vec a vec ldot vec b vec l vec mdot vec a vec mdot vec b vec m vec ndot vec a vec ndot vec b vec n| .