Vector Fields
Published On :2021-11-11 01:40:00
Vector Fields
Definition A vector field is a function F that assign to point whether it's in two dimension or three dimension
the best way to understand the vector fields is by drawing it
and we have a special notations for vector fields
F(x,y,z)=Q(x,y,z) i+ P(x,y,z) j+ R(x,y,z) k
or
F(x,y,z)=<Q(x,y,z), P(x,y,z), R(x,y,z)>
For Example:[( - 1,1) to ,,, < 1, - 1 > ]
this directional line will start at point (-1,1) and it will move 1 unit to write and 1 unit down
Important notes to remember:
Position vector is a vector from the origin to a point, so it’s like a radius of the circle that centered at the origin.
If the dot product equal zero then two vectors is perpendicular to each other.
Example 2 A vector field on R is defined by . Describe F by sketching some of the vectors F(x,y)
Solution:
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what is the dot product of our vector field with the position vector?
this shows they are perpendicular to each other therefore tangent to a circle with center the origin