Answer:
Step-by-step explanation:
Terminal points of vector u has been given as (4, 0), (9, 4).
Therefore, vector u can be represented by,
[tex]\vec{u}=\vec{u_2}-\vec{u_1}[/tex]
[tex]\vec{u}=(9i+4j)-(4i)[/tex]
[tex]\vec{u}=5i+4j[/tex]
And the magnitude of the vector u will be,
|| u || = [tex]\sqrt{5^2+4^2}[/tex]
= [tex]\sqrt{41}[/tex]
Slope of vector passing through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by the expression,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of vector u will be,
Slope = [tex]\frac{4-0}{9-4}[/tex]
= [tex]\frac{4}{5}[/tex]
Similarly, terminal points of vector v are (-7, 1) and (3, 9).
So the vector v will be,
[tex]\vec{v}=(3i+9j)-(-7i+1j)[/tex]
[tex]\vec{v}=(3i+7i)+(9j-1j)[/tex]
[tex]\vec{v}=10i+8j[/tex]
Therefore, magnitude of vector v will be,
|| v || = [tex]\sqrt{10^2+8^2}[/tex]
= [tex]\sqrt{164}[/tex]
= [tex]2\sqrt{41}[/tex]
Slope of vector v = [tex]\frac{9-1}{3+7}[/tex]
= [tex]\frac{8}{10}[/tex]
= [tex]\frac{4}{5}[/tex]