Solução_Calculo_Stewart_6e

F.
TX.10
17 VECTOR CALCULUS ET 16
17.1 Vector Fields ET 16.1
1. F(x, y) = 1 (i + j)
2
All vectors in this field are identical, with length 1 √
2
and
direction parallel to the line y = x.
3. F(x, y) =y i + 1 2 j
The length of the vector y i + 1 2 j is y 2 + 1 4 . Vectors
are tangent to parabolas opening about the x-axis.
5. F(x, y) = y i + x j
x2 + y 2
The length of the vector
y i + x j
is 1.
x2 + y2 7. F(x, y, z) =k
All vectors in this field are parallel to the z-axis and have
length 1.
9. F(x, y, z) =x k
At each point (x, y, z), F(x, y, z) is a vector of length |x|.
For x>0, all point in the direction of the positive z-axis,
while for x