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+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 + t vec b .

The vector component of vec b perpendicular to vec a is a. ( 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

The lines vec r= vec a+lambda( vec bxx vec c)a n d vec r= vec b+mu( vec cxx vec a) will intersect if a. vec axx vec c= vec bxx vec c b. vec adot vec c= vec bdot vec c c. bxx vec a= vec cxx vec a d. none of these

Prove that [ vec a , vec b , vec c+ vec d]=[ vec a , vec b , vec c]+[ vec a , vec b , vec d]

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|)

If vec b is not perpendicular to vec c , then find the vector vec r satisfying the equyation vec rxx vec b= vec axx vec b and vec r. vec c=0.

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)

If vec axx( vec bxx vec c) is perpendicular to ( vec axx vec b)xx vec c , we may have a. ( vec a. vec c)| vec b|^2=( vec a. vec b)( vec b.vec c)( vec c.vec a) b. vec adot vec b=0 c. vec adot vec c=0 d. vec bdot vec c=0

If vec adot vec b= vec adot vec c\ a n d\ vec axx vec b= vec axx vec c ,\ vec a!=0, then

If vec a= vec b+ vec c , vec b X vecd= vec0 and vec c*vec d=0 then ( vec dx( vec ax vec d))/( vec d^2) is equal to (a) vec a (b) vec b (c) vec c (d) vec d