Question

quantity
(D) 3
4. The gradient of a scalar field at any point is always a
(A) Scalar
(B) Vector
(C) Can be both (a) or (b)
(D) None​

Answer 1

Answer:

(c) can be both (a) or (b)

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The gradient of a scalar field at any point is always a

(A) Scalar

(B) Vector

(C) Can be both (a) or (b)

(D) None

EVALUATION

Gradient

Let a scalar field be defined by the scalar function f(x, y, z) of coordinates x , y , z which is also defined and differentiable at each point (x , y , z) in some region of space.

Then gradient of the function is defined as

$\displaystyle\nabla f = \bigg(\hat{i} \frac{ \partial}{ \partial x} + \hat{j} \frac{ \partial}{ \partial y} + \hat{k} \frac{ \partial}{ \partial z} \bigg)f$

Thus we see that the gradient of a scalar field at any point is always a vector

FINAL ANSWER

Hence the correct option is (B) Vector

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