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67. Explain why or why not Determine whether the following state- ments are true and give an explanation or counterexample. a

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Answer #1

1) False .

Gradient of scalar function is always vector ..

Here

F​​​​​​x = 2x

F​​​​​​y = 2y

Gradient F= Fx I + Fy j = 2xi + 2yj

(2) false

Gradient gives the direction of maximum rate of change of function it can bhi positive or negative

(3) false

Gradient of above function has 3 Component

Gradient F = Fxi +Fyj + Fzk

(4) .True

Gradient F = Fx i + Fy j + Fz k = 0+0+0= 0

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