Complete question is;
What is the magnitude and direction of (-3.7i) + (7.4j)?
Answer:
Magnitude = 8.27
Direction = 116.57°
Step-by-step explanation:
Magnitude of the vector will be;
|R| = √((-3.7²) + (7.4²))
|R| = √68.45
|R| = 8.27
Direction will be;
tan θ = 7.4/-3.7
tan θ = -2
θ = tan^(-1) -2
θ = -63.43°
Angle is negative but we can't present it as such.
Now, in the second and fourth quadrants, tan θ has a negative value.
However, from the components of the vector we are given, we see that we work here in the 2nd quadrant since the i vector is negative and j vector is positive. Therefore, a reference angle of 63.43° means that the actual angle is 63.43° above the negative x axis and can be written in standard form as;
180 − 63.43 = 116.57°
