A line `l` is passing through the point ` vec b` and is parallel to vector `vecc` 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 c|^2) vec c` or `(|( vec b- vec a)xx vec c|)/(|vecc|)` .

Show that the perpendicular distance of a point A(vec a) from the line vec r=vec b+tvec c is |(vec b-vec a)xxvec c||vec c|

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

Show that distance of the point vec c from the line joining vec a and vec b is (|vec b xxvec c+vec c xxvec a+vec a xxvec b)/(|vec b-vec a|)

[[vec a + vec b-vec c, vec b + vec c-vec a, vec c + vec a-vec b is equal to

For any three vectors vec a, vec b, vec c, (vec a-vec b) * (vec b-vec c) xx (vec c-vec a) is equal to

vec a * {(vec b + vec c) xx (vec a + 2vec b + 3vec c)} = [vec with bvec c]

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)

For any three vectors vec a;vec b;vec c find [vec a+vec b;vec b+vec c;vec c+vec a]

vec a + 2vec b + 3vec c = vec 0 and vec a xxvec b + vec b xxvec c + vec c xxvec a = l (vec b xxvec c) then l =

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|)