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

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 line : passing through the point vec c , parallel to the plane vec r *vec n = p and intersecting the line vec r =vec a + t vec b .

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 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

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

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.

The equation of the plane which passes through the line of intersection of planes vec r. vec n_1=, q_1, vec r. vec n_2=q_2 and the is parallel to the line of intersection of planers vec r. vec n_3=q_3a n d vec r. 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\