Answer: magnitude = 5 and angle = 160°
Explanation:
A vector has magnitude 5 and angle -20°
A vector can be written in terms of its components as :
[tex]\vec{A}=A_x\hat{i}+A_y\hat j \\ \Rightarrow \vec A = A cos\theta \hat i+A sin\theta \hat j[/tex]
using trigonometry identity:
sin θ = -sin ( 180 + θ )
cos θ = - cos (180 + θ)
Thus, we can write the same vector as:
[tex]\vec A = -A cos(180+\theta) \hat i+(-A) sin(180+\theta) \hat j[/tex]
Magnitude [tex]|A|=\sqrt{(-A)^2+(-A)^2} = A = 5[/tex]
Thus, the magnitude would be A = 5 and angle = 180+θ= 180-20 = 160°
