Answer:
90°
Step-by-step explanation:
First you must calculate the module or the magnitude of both vectors
The module of u is:
[tex]|u|=\sqrt{(8)^2 + (-3)^2} \\\\|u|=\sqrt{64 + 9}\\\\|u|=8.544[/tex]
The module of v is:
[tex]|v|=\sqrt{(-3)^2 + (-8)^2} \\\\|u|=\sqrt{9 + 64}\\\\|u|=8.544[/tex]
Now we calculate the scalar product between both vectors
[tex]u*v = 8*(-3) + (-3)*(-8)\\\\u*v = -24+ 24=0[/tex]
Finally we know that the scalar product of two vectors is equal to:
[tex]u*v = |u||v|*cos(\theta)[/tex]
Where [tex]\theta[/tex] is the angle between the vectors u and v. Now we solve the equation for [tex]\theta[/tex]
[tex]0 = 8.544*8.544*cos(\theta)\\\\0 = cos(\theta)\\\\\theta= arcos(0)\\\\\theta=90\°[/tex]
the answer is 90°
Whenever the scalar product of two vectors is equals to zero it means that the angle between them is 90 °
