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.

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

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.

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) .

If vec rdot vec a=0, vec rdot vec b=1a n d[ vec r vec a vec b]=1, vec adot vec b!=0,( vec adot vec b)^2-=| vec a|^2| vec b|^2=1, then find vec r in terms of vec aa n d vec bdot

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

The condition for equations vec rxx vec a= vec ba n d vec rxx vec c= vec d to be consistent is vec bdot vec c= vec adot vec d b. vec adot vec b= vec cdot vec d c. vec bdot vec c+ vec adot vec d=0 d. vec adot vec b+ vec cdot vec d=0

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

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