Show that the distance `d` from point `P` to the line `l` having equation ` vec r= vec a+lambda vec b` is given by `d=(| vec bxx vec P Q|)/(| vec s|),w h e r eQ` is any point on the line `ldot`

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

Show that distance of the point vec c from the line joining vec a and vec b is (|vec b xxvec c+vec c xxvec a+vec a xxvec b)/(|vec b-vec a|)

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

If vec P xx vec Q= vec R, vec Q xx vec R= vec P and vec R xx vec P = vec Q then

If vec p = vec a + vec b, vec q = vec a-vec b | vec a | = | vec b | = 1 then | vec p xxvec q | =

Show that the perpendicular distance of a point A(vec a) from the line vec r=vec b+tvec c is |(vec b-vec a)xxvec c||vec c|

Write the position vector of the point where the line vec r= vec a+lambda vec b meets the plane vec r dot (vec n)=0.

if vec(P) xx vec(R ) = vec(Q) xx vec(R ) , then

The length of the perpendicular form the origin to the plane passing through the point a and containing the line vec r= vec b+lambda vec c is a. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c+ vec cxx vec a|) b. ([ vec a vec b vec c])/(| vec axx vec b+ vec bxx vec c|) c. ([ vec a vec b vec c])/(| vec bxx vec c+ vec cxx vec a|) d. ([ vec a vec b vec c])/(| vec cxx vec a+ vec axx vec b|)

If vec P+ vec Q = vec R and |vec P| = |vec Q| = | vec R| , then angle between vec P and vec Q is