Question

Let r = x i + y j + z k and r = |r|.

Verify each identity.

Answer 1

Step 1 :

The vector is and .

Find r .

(a)

The equation is .

Consider .

Substitute in above equation.

Therefore, .

Step 2 :

(b)

The equation is .

Consider .

Therefore, .

Step 3 :

 (c)

The equation is .

Consider .

Apply chain rule of partial derivatives : .

Substitute in above equation.

Therefore, .

Step 4 :

(d)

The equation is .

Consider .

Apply chain rule of partial derivatives : .

Substitute in above equation.

Therefore, .

Solution :

(a) .

(b) .

(c) .

(d) .