Answer:
a. [tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]
Step-by-step explanation:
The given vector is v= 4i - 5j
The magnitude of this vector is;
[tex]|v|=\sqrt{(-4)^2+(-5)^2}[/tex]
[tex]|v|=\sqrt{16+25}[/tex]
[tex]|v|=\sqrt{41}[/tex]
The unit vector u in the direction of v is;
[tex]u=\frac{v}{|v|}[/tex]
[tex]u=\frac{4i - 5j}{\sqrt{41}}[/tex]
[tex]u=\frac{4i }{\sqrt{41}}-\frac{5j}{\sqrt{41}}[/tex]
We rationalize to get
[tex]u=\frac{4\sqrt{41}i }{41}-\frac{5\sqrt{41}j}{41}[/tex]
