For the following exercises, solve the problem. 307. The electrical potential (voltage) in a certain region of space is given by the function V ( x , y , z ) = 5 x 2 − 3 x y + x y z . a. Find the rate of change of the voltage at point (3. 4. 5) in the direction of the vector ( 1. 1. —1) b. In which direction does the voltage change most rapidly at point (3. 4. 5)? c. What is the maximum rate of change of the voltage at point (3, 4. 5)?
For the following exercises, solve the problem. 307. The electrical potential (voltage) in a certain region of space is given by the function V ( x , y , z ) = 5 x 2 − 3 x y + x y z . a. Find the rate of change of the voltage at point (3. 4. 5) in the direction of the vector ( 1. 1. —1) b. In which direction does the voltage change most rapidly at point (3. 4. 5)? c. What is the maximum rate of change of the voltage at point (3, 4. 5)?
307. The electrical potential (voltage) in a certain region of space is given by the function
V
(
x
,
y
,
z
)
=
5
x
2
−
3
x
y
+
x
y
z
.
a. Find the rate of change of the voltage at point (3. 4. 5) in the direction of the vector ( 1. 1. —1)
b. In which direction does the voltage change most rapidly at point (3. 4. 5)?
c. What is the maximum rate of change of the voltage at point (3, 4. 5)?
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
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