Answer:
see below
Explanation:
Here, we'll use an ordered pair <a, b> to represent each vector's two components. The rules are ...
- multiplying a vector by a scalar multiplies each component by that scalar
- multiplying a vector by a scalar multiplies its magnitude by the magnitude of the scalar
- the magnitude of a vector is the square root of the sum of the squares of its components
1.
For A = <2.5, -3.5>, |A| = √(2.5²+(-3.5)²) = √18.5 ≈ 4.30
- 2A = <5, -7>; |2A| = 8.60
- -2A = <-5, 7>; |-2A| = 8.60
- A/2 = <1.25, -1.75>; |A/2| = 2.15
_____
2.
A = |A|<cos(43.9°), sin(43.9°)>
B = |B|<cos(154.8°), sin(154.8°)>
C = <0, -25.8>
The sum being zero gives rise to 2 equations in 2 unknowns.
|A|cos(43.9°) +|B|cos(154.8°) = 0
|A|sin(43.9°) +|B|sin(154.8°) = 25.8
Using Cramer's rule to find the solution, we get ...
|A| = 25.8cos(154.8°)/(cos(154.8°)sin(43.9°) -sin(154.8°)cos(43.9°))
|A| = 25.8cos(154.8°)/sin(43.9° -154.8°)
|A| ≈ 24.9887
|B| = -25.8cos(43.9°)/sin(-110.9°)
|B| ≈ 19.8995