E- - V - x - - V - y - - V - z k- here negative sign signifies that

The correct option is D E⃗ is directed in the direction of decreasing V E⃗= ∂ V∂ x ∂ v∂ y ∂ v∂ zk̂ it shows direction of ε⃗ is in the direc ...

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Standard VIII

Mathematics

Solving Equations with Variables on Both Sides

E⃗=⃗ -∂ V ∂ x...

Question

$\to E = - \frac{\partial V}{\partial x}^i - \frac{\partial V}{\partial y}^j - \frac{\partial V}{\partial z}^k$ , here negative sign signifies that

Direction of

\to E

is opposite to

V

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\to E

is negative

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\to E

increases as

V

decreases

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\to E

is directed in the direction of decreasing

V

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Solution

The correct option is D $\to E$ is directed in the direction of decreasing $V$
$\to E = \frac{- \partial V}{\partial x}^ı - \frac{\partial v}{\partial y}^ȷ - \frac{\partial v}{\partial z}^k$
it shows direction of $\to ε$
is in the direction of
where $v$ is decreasing.
Answer: (D)
$\to ε$ is directed in the direction of dec. V

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→E=−∂V∂x^i−∂V∂y^j−∂V∂z^k, here negative sign signifies that

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