If Ø(x, y, z) = x² - y²-2²-2, then ∇Ø at (2,1,-1) is
A) 4i +2j-2k
B)4i-2j-2k
C) 4i + 2j + 2k
D)4i - 2j +2k
Ø(x,y,z)=x2−y2−z2−2Then ∇Ø=∂∂xi,∂∂xj,∂∂xk∇Ø=∂∂x(x2−y2−z2−2),∂∂x(x2−y2−z2−2),∂∂x(x2−y2−z2−2)∇Ø=2xi,2yj,2zkAt(2,1,−1)∇Ø=4i+2j−2kØ(x, y, z) = x² - y²-z²-2\\ Then \space ∇Ø= \frac{\partial}{\partial x}i, \frac{\partial}{\partial x}j, \frac{\partial}{\partial x}k\\ ∇Ø= \frac{\partial}{\partial x} (x² - y²-z²-2), \frac{\partial}{\partial x}(x² - y²-z²-2), \frac{\partial}{\partial x}(x² - y²-z²-2)\\ ∇Ø=2x i, 2yj,2zk\\ At (2,1,-1) \\ ∇Ø=4 i+ 2j-2kØ(x,y,z)=x2−y2−z2−2Then ∇Ø=∂x∂i,∂x∂j,∂x∂k∇Ø=∂x∂(x2−y2−z2−2),∂x∂(x2−y2−z2−2),∂x∂(x2−y2−z2−2)∇Ø=2xi,2yj,2zkAt(2,1,−1)∇Ø=4i+2j−2k
Option A is correct.
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