Show that equation of the plane passing through a point having position vector `vec(a)` and parallel to `vec(b)` and `vec(c)` is `vec(r) = vec(a) + lambda vec(b) + mu vec(c)` .

Show that the points having position vectors vec(a), vec(b),(vec(c)=3 vec(a)- 2 vec(b)) are collinear, whatever be 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

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

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+tvec c is a.vec r=vec a+lambda(vec n xxvec c) b.(vec r-vec a)xx(vec n xxvec c) c.vec r=vec b+lambda(vec n xxvec c) d.none of these

Show that the points whose position vectors are vec(a) + 2vec(b) + 5vec(c), 3vec(a) + 2vec(b) + vec(c), 2vec(a) + 2vec(b) + 3vec(c) are colliner.

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|)

Show that the points having position vectors (-2vec(a) + 3 vec(b)+5vec(c)),(vec(a)+ 2 vec(b)+ 3 vec(c)) and (7vec(a)- vec(c)) are collinear, whatever be vec(a),vec(b),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

The equation of the plane containing the parallel lines vec r=vec a+tvec c and vec r=vec b+phivec c is

A vector equation of the line of intersection of the planes vec r = vec b + lambda_ (1) (vec b-vec a) + mu_ (1) (vec a + vec c) vec r = vec c + lambda_ (2) (vec b-vec c) + mu_ (2) (vec a + vec b) and vec a, vec b, vec c being non coplanar vectors is