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 lines vec r=a_(1)+lambdavec b and vec r=vec a_(2)+muvec b is

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

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|)

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

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.

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

A Show that equation of angle bisectors of line vec r = a + lambdavec b and vec r = vec b + muvec a are vec r = (vec a + vec b) + gamma (| vec b | vec a | vec a)

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

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

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