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 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|)

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

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 axx vec b= vec bxx vec c!=0,\ then show that vec a+ vec c=m vec b ,\ w h e r e\ m is any scalar.

Write the condition for the lines vec r= vec a_1+lambda vec b_1 a n d\ vec r= vec a_2+mu vec b_2dot\ to be intersecting.

If vec axx vec b= vec bxx vec c!=0 , then show that vec a+ vec c=m vec b , where m is any scalar.

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|)

Write the formula for the shortest distance between the lines vec r= vec a_1+lambda vec b_1 a n d\ vec r= vec a_2+mu vec b_2dot\

If vec axx vec b= vec cxx vec da n d vec axx vec c= vec bxx vec d , then show that vec a- vec d , is paralelto vec b- vec c