Directions of zero change Find the directions in the xy-plane in which the following functions have zero change at the given point. Express the directions in terms of unit vectors. 67. f ( x , y ) = 3 + 2 x 2 + y 2 ; P ( 1 , − 2 , 3 )
Directions of zero change Find the directions in the xy-plane in which the following functions have zero change at the given point. Express the directions in terms of unit vectors. 67. f ( x , y ) = 3 + 2 x 2 + y 2 ; P ( 1 , − 2 , 3 )
Solution Summary: The author explains the direction in which the function f(x,y)=sqrt3+2x2
Directions of zero changeFind the directions in the xy-plane in which the following functions have zero change at the given point. Express the directions in terms of unit vectors.
67.
f
(
x
,
y
)
=
3
+
2
x
2
+
y
2
;
P
(
1
,
−
2
,
3
)
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.
Describe the graph of the equation.
r = (6 – 21) i+ 10rj
O It is a line in 2-space through the point (6, 2) and parallel to the vector V = 10j.
O Itis a plane in 2-space through the point (-2, 10) and parallel to the vector v = 6i.
O Itis a line in 2-space through the point (6, 0) and parallel to the vector v = - 2i+ 10j.
O Itis a line in 2-space through the point (-2, 10) and parallel to the vector v = 6i.
O It is a plane in 2-space through the point (6, 0) and parallel to the vector v = -2i + 10j.
Describe the graph of the equation.
r= (3 – 21) i + 61j
It is a line in 2-space through the point (3, 2) and parallel to the vector v = 6j.
O Itis a line in 2-space through the point (-2, 6) and parallel to the vector v = 3i
O t isa plane in 2-space through the point (3, 0) and parallel to the vector v = -2i+ 6j.
O Itis a line in 2-space through the point (3, 0) and parallel to the vector v = -2i+6j.
O tis a plane in 2-space through the point (-2, 6) and parallel to the vector v = 31.
e) a unit vector perpendicular to
f) the volume of the parallelepiped formed
both i and i
by vectors ū, w and v
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University Calculus: Early Transcendentals (4th Edition)
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