x, y, z) are the coordinates of the points inside the box. (a) Find the rate of change at the point (1, −2, 2) in the direction of a unit vector at an angle −π/6 to the positive x-axis, π/2 to the negative y-axis, and do Angle π/3 to the negative z-axis (b) Find the unit vector with the direction in which the point (1,−2,2) decreases the most (fastest) and give the magnitude of the change.
x, y, z) are the coordinates of the points inside the box. (a) Find the rate of change at the point (1, −2, 2) in the direction of a unit vector at an angle −π/6 to the positive x-axis, π/2 to the negative y-axis, and do Angle π/3 to the negative z-axis (b) Find the unit vector with the direction in which the point (1,−2,2) decreases the most (fastest) and give the magnitude of the change.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(x, y, z) are the coordinates of the points inside the box.
(a) Find the rate of change at the point (1, −2, 2) in the direction of a unit vector at an angle −π/6 to the positive x-axis, π/2 to the negative y-axis, and do Angle π/3 to the negative z-axis
(b) Find the unit vector with the direction in which the point (1,−2,2) decreases the most (fastest) and give the magnitude of the change.
Transcribed Image Text:1
W (x, y, z) =
x² + y² + z²
.2
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