Name the property
to=0
+
4 = 1
T4
Answers
Answer:
Vector notation. In 18.04 we will mostly use the notation (v) = (a, b) for vectors. The
other common notation (v) = ai + bj runs the risk of i being confused with i =√−1
–especially if I forget to make i boldfaced.
Definition. A vector field (also called called a vector-valued function) is a function F(x, y)
from R2
to R2
. That is,
F(x, y) = (M(x, y), N(x, y)),
where M and N are regular functions on the plane. In standard physics notation
F(x, y) = M(x, y)i + N(x, y)j = (M, N).
Algebraically, a vector field is nothing more than two ordinary functions of two variables.
Example GT.1. Here are a number of standard examples of vector fields.
(a.1) Force: constant gravitational field F(x, y) = (0, −g).
(a.2) Velocity:
V(x, y) = x*x(2 + y)2,yx2 + y2= xr2,yr2.
(Here r is our usual polar r.) It is a radial vector field, i.e. it points radially away from the
origin. It is a shrinking radial field –like water pouring from a source at (0,0).
This vector field exhibits another important feature for us: it is not defined at the origin
because the denominator becomes zero there. We will say that V has a singularity at the
origin.
(a.3) Unit tangential field: F = (−y, x) /r. Tangential means tangent to circles centered
at the origin. We know it is tangential because it is orthogonal to the radial vector field in
(a.2). F also has a singularity at the origin. We
(a.4) Gradient field: F = ∇f, e.g., f(x, y) = xy2 ⇒ ∇f =y2, 2xy
"HOPE THIS HELPED YOU"
Answer: IDK
Step-by-step explanation: I M NOT STONG AT MATH