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

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)

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

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 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

Value of [ vec axx vec b , vec axx vec c , vec d] is always equal to a. ( vec adot vec d)[ vec a vec b vec c] b. ( vec adot vec c)[ vec a vec b vec d] c. ( vec adot vec b)[ vec a vec b vec d] d. none of these

If vec a . vec b=beta and vec axx vec b= vec c ,then vec b is ((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)

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

If vec a is parallel to vec bxx vec c , then ( vec axx vec b) . ( vec axx vec c) is equal to a. | vec a|^2( vec b . vec c) b. | vec b|^2( vec a . vec c) c. | vec c|^2( vec a . 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