Show that distance of the point ` vec c` from the line joining ` vec aa n d vec b` is `(| vec bxx vec c+ vec cxx vec a+ vec axx vec b)/(| vec b- vec a|)`

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|)

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

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

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|

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

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

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

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|)

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

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n vec adot vec b+ vec bdot vec c+ vec cdot vec a=0 b. vec axx vec b= vec bxx vec c= vec cxx vec a c. vec adot vec b= vec bdot vec c= vec cdot vec a d. vec axx vec b+ vec bxx vec c+ vec cxx vec a=0