The vector equation of the plane passing through the origin and the line of intersection of the planes ` vec rdot vec a=lambdaa n d vec rdot vec b=mu` is (a) ` vec rdot(lambda vec a-mu vec b)=0` (b) ` vec rdot(lambda vec b-mu vec a)=0` (c) ` vec rdot(lambda vec a+mu vec b)=0` (d) ` vec rdot(lambda vec b+mu vec a)=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

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

The equation of the plane which passes through the line of intersection of planes vec rdot vec n_1=, q_1, vec rdot vec n_2=q_2 and the is parallel to the line of intersection of planers vec rdot vec n_3=q_3a n d vec rdot vec n_4-q_4 is

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\

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

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.

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.

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

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

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|)