Answer:
1. Approximately 5.83 units
2. Approximately 59.04°
Step-by-step explanation:
Given two vectors [tex]\vec{u}=(5,2)[/tex] and [tex]\vec{v}=(2,-3).[/tex]
To find the difference [tex]\vec{u}-\vec{v}[/tex] just subtract coordinates of vector v from coordinates of vector u:
[tex]\vec{u}-\vec{v}=(5-2,2-(-3))=(3,5)[/tex]
1. The magnitude of the vector [tex]\vec{u}-\vec{v}[/tex] is
[tex]|\vec{u}-\vec{v}|=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}\approx 5.83\ units[/tex]
2. Find tangent of angle which vector [tex]\vec{u}-\vec{v}=(3,5)[/tex] forms with x-axis:
[tex]\tan \alpha=\dfrac{5}{3}\\ \\\alpha \approx 59.04^{\circ}[/tex]
