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

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 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 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 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 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 a , vec b , vec c are non-coplanar vector and lambda is a real number, then the vectors vec a+2 vec b+3 vec c ,lambda vec b+mu vec ca n d(2lambda-1) vec c are coplanar when a. mu in R b. lambda=1/2 c. lambda=0 d. no value of lambda

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

A vector vec d is equally inclined to three vectors vec a= hat i+ hat j+ hat k , vec b=2 hat i+ hat ja n d vec c=3 hat j-2 hat kdot Let vec x , vec y ,a n d vec z be three vectors in the plane of vec a , vec b ; vec b , vec c ; vec c , vec a , respectively. Then a. vec x. vec d=-1 b. vec y. vec d=1 c. vec z. vec d=0 d. vec r. vec d=0,w h e r e vec r=lambda vec x+mu vec y+delta vec z

Statement 1: Lines vec r= hat i+ hat j- hat k+lambda(3 hat i- hat j)a n d vec r=4 hat i- hat k+mu(2 hat i++3 hat k) intersect. Statement 2: vec bxx vec d=0 , then lines vec r= vec a+lambda vec ba n d vec r= vec c+lambda vec d do not intersect.