Question

Let A be a constant vector and R be the position vector. Prove that div (Ax R) =0.​

Answer 1

Answer:

If vector r is the position vector of any point (x, y, z) and vector A is a constant vector then show that (i) vector(r.A).A = 0 is the equation of a constant plane. (ii) vector(r-A).r the equation of a sphere. Also show that result of (i) is of the form Ax + By + Cz + D = 0 where D = -(A2 + B2 + C2) and that of (ii) is of the from x2 + y2 + z2 = r2.Read more on Sarthaks.com - https://www.sarthaks.com/447483/vector-the-position-vector-point-and-vector-constant-vector-then-show-that-vector-equation