HELP HELP 1 QUESTION!! ILL MARK AS BRAINLIST IF CORRECT AND EXPLAINED
1 answer:
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<h2>Answer:</h2>
a. <-13/2,-13/2>
<h2>Step-by-step explanation:</h2>The projection of a vector u onto another vector v is given by;
=
----------------(i)
Where;
u.v is the dot product of vectors u and v
|v| is the magnitude of vector v
Given:
u = <-6, -7>
v = <1, 1>
These can be re-written in unit vector notation as;
u = -6i -7j
v = i + j
<em>Now;</em>
<em>Let's find the following</em>
(i) u . v
u . v = (-6i - 7j) . (i + j)
u . v = (-6i) (1i) + (-7j)(1j) [Remember that, i.i = j.j = 1]
u . v = -6 -7 = -13
(ii) |v|
|v| =
|v| =
<em>Substitute these values into equation (i) as follows;</em>
=
=
This can be re-written as;
=
=
When 
, you have 
.
When
, you have 
.
Clearly,
.
Assume
. Now when 
, you have
Therefore by induction the sequence is monotone (decreasing).
When
Clearly,
Assume
Therefore by induction the sequence is monotone (decreasing).