If vector a, vector b, vector c are position vectors of the vertices A, B and C respectively, of a triangle ABC, write the value of vector(AB)

Question

If  \(\vec a,\,\vec b, \,\vec c \) are position vectors of the vertices A, B and C respectively, of a triangle ABC, write the value of  \(\vec {AB}+\vec{BC}+\vec{CA}.\)

Answer 1

Any vector \(\vec{AB},\) if the position vectors of point A(\(\vec a\)) and B(\(\vec b\))  are known, can be written as  \(\vec b-\vec a\).

Since the position vectors of points A, B, C are \(\vec a,\,\vec b, \,\vec c \), we get