|V| = 10.33 units and the direction θ = -47.35° or 312.65°.
Given the x and y components of a vector, we can calculate the magnitude and direction from these components.
Applying the Pythagorean theorem we have that the magnitude of the vector is:
|V| = [tex]\sqrt{Vx^{2}+Vy^{2} }[/tex]
|V| = [tex]\sqrt{(7.00units)^{2}+(-7.60units)^{2}} = \sqrt{106units^{2}} = 10.33units[/tex]
The expression for the direction of a vector comes from the definition of the tangent of an angle:
tan θ = [tex]\frac{Vy}{Vx}[/tex] ------> θ = arc tan [tex]\frac{Vy}{Vx}[/tex]
θ = arc tan [tex]\frac{-7.60units}{7.00units}[/tex]
θ = -47.35° or 312.65°
