If we know the vector A, what now is the vector minus A?
A equals A of x x roof plus A of y y roof
plus A of z z roof.
This is the component of A in the x direction, component of
A in the y direction, component
of A in the z direction.
If you want to know what minus A is, you multiply left and
right with a minus sign.
So you get minus A equals minus A of x x roof minus A of
y y roof minus A of z z roof.
Notice that the x component of this vector
has flipped 180 degrees.
What was first in the plus x direction, assuming that A of
x is positive, is now in the minus x direction.
What was first in the plus y direction, assuming that A of
y was positive is now in the minus y direction.
So each of these individual vectors--
this is a vector in the x direction, this is a vector in
the y direction, and this is a vector in the z direction--
each one of these flip over 180 degrees.
So the conclusion is that minus A is also flipped 180
degrees relative to plus A.