Answer:

Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if
. Recall that given two vectors a,b a⊥ b if and only if
where
is the dot product defined in
. Suposse that
. We want to find γ such that
. Given that the dot product can be distributed and that it is linear, the following equation is obtained

Recall that
are both real numbers, so by solving the value of γ, we get that

By construction, this γ is unique if
, since if there was a
such that
, then

Given:
The power generated by an electrical circuit (in watts) as function of its current x (in amperes) is modeled by:

To find:
The current that will produce the maximum power.
Solution:
We have,

Here, leading coefficient is negative. So, it is a downward parabola.
Vertex of a downward parabola is the point of maxima.
If a parabola is
, then

In the given function, a=-12 and b=120. So,



Putting x=5 in the given function, we get




Therefore, 5 watt current will produce the maximum power of 300 amperes.
I believe it is proposition