Answer:
144.2°
Step-by-step explanation:
You want the angle between these vectors:
Angle
The angle between the vectors can be found a number of ways. One we like is the angle of the ratio when they are expressed as complex numbers:
(-3+8i)/(6 -4i) = (-3+8i)(6+4i)/(something real) = (-18-32 +48i +12i)
= (-50 +36i)/(real number)
Then the angle is ...
arctan(36/(-50)) ≈ 180° -35.8° = 144.2°
The angle between the vectors is about 144.2°.
Alternate solution (1)
Another way to find the angle is to find the difference of the angles of the vectors relative to the i direction.
arctan(8/(-3)) -arctan(-4/6) = (180 -69.444)° -(-33.690°) = 144.2°
Alternate solution (2)
You can make use of the dot product relation:
u•v = |u|·|v|·cos(angle)
Solving for the angle, we have ...
angle = arccos(u•v/(|u|·|v|))
angle = arccos((-3·6 +8·(-4))/√((3²+8²)(6²+4²)) = arccos(-50/√(73·52))
= arccos(-50/√3796) ≈ arccos(-0.811534)
angle ≈ 144.2°
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Additional comment
The "something real" in the first solution is (6 -4i)(6 +4i) = 6² +4² = 52. Its value does not change the angle, so is irrelevant.
The arctangent function only gives angle values in the range -90° to +90°. The only way the angle of vector u can be properly found is by considering the quadrant in which it must lie. If you're using a spreadsheet to find the angle, the ATAN2(x, y) function is appropriate. It takes quadrant into consideration (and returns the angle in radians).
As the second attachment shows, the angle is 144.2° when rounded to tenths. It is 144.25° when rounded to hundredths, which can be confusing, since 144.25° would round to 144.3°.
The first attachment shows the angle found using a geometry app to plot the vectors and display the angle.
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