Find the point in which the plane `vec r =vec a-vec b+ m(vec a +vec b-vec c)+ n(vec a + vec c -vec b)` is cut by the line through the point `2 vec a +3vec b` and parallel to `vec c`

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

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

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

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

Show that the points with position vectors vec a-2vec b+3vec c,-2vec a+3vec b-vec c and 4vec a-7vec b+7vec c are collinear.

If vec a + vec b = vec c and | vec a | = | vec b | = | vec c | find the angle between vec a and vec b

Show that the point A,B,C with position vectors vec a-2vec b+3vec c,2vec a+3vec b-4vec c and -7vec b+10vec c are collinear.

If |vec a|+|vec b|=|vec c| and vec a+vec b=vec c, then find the angle between vec a and vec b

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|)

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|)