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.`

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

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

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\

Write the equation of the plane vec r= vec a+lambda vec b+mu vec c\ in scalar product form.

Write a vector normal to the plane vec r=l vec b+m vec c

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 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.

A straight line vecr=veca+lambda vecb meets the plane vecr. vec n=0 at p. Then position vector of P is

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 expression in the vector form for the point vec r_1 of intersection of the plane vec rdot vec n=d and the perpendicular line vec r= vec r_0+t vec n where t is a parameter given by