Question

If A is a constant vector, then prove that ∇(r . A)=A.​

Answer 1

Explanation:

I hope this answers help you

Answer 2

Answer: r is a vector quantity and is given by

$r=xi+yj+zk$

A is a constant vector and is given by

$A_{x}i+A_{y}j+A_{z}k$

Explanation:

To prove:-

∇(r . A)=A

Given:-

r is a vector quantity and is given by

$r= xi+yj+zk$

A is a constant vector and is given by

$A=A_{x}i+A_{y}j+A_{z}k$

$r.A=(xi+yj+zk).(A_{x}i+A_{y}j+A_{z}k)$

$r.A= A_{x}x+A_{y}y+A_{z}z$

Taking the delta function

∇(r.A)= $\frac{dA_{x}x}{dx}i+\frac{dA_{y}y}{dy}j+\frac{dA_{z}z}{dz}k$

∇(r.A)=$A_{x}i+A_{y}j+A_{z}k$

∇(r.A)=A

Hence proved.