Answer:
7.2∠169°
Step-by-step explanation:
You want the magnitude and direction of the sum of the vectors u(6; 135°) and v(4; 225°).
Sum
A suitable calculator will tell you the sum is ...
u + v = (7.2; 169°)
Components
In component form, the sum is ...
(6cos(135°) +4cos(225°), 6sin(135°) +4sin(225°)) = (-5√2, √2)
Then the magnitude and angle are ...
|u+v| = √((-5√2)² +(√2)²) = √52 ≈ 7.2
art(u+v) = arctan((√2)/(-5√2)) = arctan(-1/5) ≈ 169° . . . . 2nd quadrant
The magnitude is about 7.2 units; the direction is about 169°.
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Additional comment
Many scientific and graphing calculators can do vector arithmetic in component and/or magnitude/angle form. Since you need a calculator anyway, it makes sense to use the full capability.
There are a number of ways that vectors can be expressed in magnitude and direction form. They include ...
- 6(cos(135°), sin(135°)) . . . . . . . used in your problem statement
- 6(cos(135°) +i·sin(135°))
- 6cis(135°) . . . . . . an abbreviation of the preceding
- 6∠135°
- (6; 135°) . . . . . . . note the use of semicolon as a separator
- [6, 135] . . . . . and you have to remember this is [magnitude, angle] with angle in degrees (not radians)
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