Answer :
Answer:
a. <-13/2,-13/2>
Step-by-step explanation:
The projection of a vector u onto another vector v is given by;
[tex]proj_vu[/tex] = [tex](\frac{u.v}{|v|^2})v[/tex] ----------------(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
Now;
Let's find the following
(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| = [tex]\sqrt{(1)^2 + (1)^2}[/tex]
|v| = [tex]\sqrt{2}[/tex]
Substitute these values into equation (i) as follows;
[tex]proj_vu[/tex] = [tex][\frac{-13}{(\sqrt{2}) ^2}][i + j][/tex]
[tex]proj_vu[/tex] = [tex]\frac{-13}{2} [i + j][/tex]
This can be re-written as;
[tex]proj_vu[/tex] = [tex]\frac{-13}{2}i + \frac{-13}{2}j[/tex]
[tex]proj_vu[/tex] = [tex]<\frac{-13}{2}, \frac{-13}{2}>[/tex]