The equation of a line passing through the point ` vec a` parallel to the plane ` vec rdot 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

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+tvec b

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then vec b= vec c b. vec b=0 c. vec b+ vec c=0 d. none of these

If vec a + vec b + vec c = 0, prove that (vec a xx vec b) = (vec b xx vec c) = (vec c xx vec a)

The vector component of vec b perpendicular to vec a is ( vec bdot vec c) vec a b. ( vec axx( vec bxx vec a))/(| vec a|^2) c. vec axx( vec bxx vec a) d. none of these

Let lambda = vec a xx (vec b + vec c), vec mu = vec b xx (vec c + vec a) and vec nu = vec c xx (vec a + vec b). Then

[vec a + vec b, vec b + vec c, vec c + vec a] = 2 [vec a, vec b, vec c]

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

A line l is passing through the point vec b and is parallel to vector vec c Determine the distance of point A(vec a) from the line l in the form vec b-vec a+((vec a-vec b)vec c)/(|vec a|^(2))vec c or (|(vec b-vec a)xxvec c|)/(|vec c|)

vec r=vec linesvec r=vec a+lambda(vec b xxvec c) and vec r=vec b+mu(vec c xxvec a) will intersect if a.vec a xxvec c=vec b xxvec c b.vec a*vec c=vec b*vec c c.b xxvec a=vec c xxvec a d.none of these

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|)