Question 1173576: Find the component form of the sum of u and v with the given magnitudes and direction angles 𝜃u and 𝜃v.(Round all values to two decimal places.
Magnitude Angle
u = 35
v= 52
𝜃u = 25°
𝜃v = 120°
u + v = ___
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's find the component form of the vectors u and v, and then find their sum.
**1. Find the component form of vector u**
* Magnitude of u: |u| = 35
* Direction angle of u: θu = 25°
* x-component of u: u_x = |u| * cos(θu) = 35 * cos(25°) ≈ 35 * 0.9063 ≈ 31.72
* y-component of u: u_y = |u| * sin(θu) = 35 * sin(25°) ≈ 35 * 0.4226 ≈ 14.79
Therefore, u ≈ <31.72, 14.79>
**2. Find the component form of vector v**
* Magnitude of v: |v| = 52
* Direction angle of v: θv = 120°
* x-component of v: v_x = |v| * cos(θv) = 52 * cos(120°) = 52 * (-0.5) = -26
* y-component of v: v_y = |v| * sin(θv) = 52 * sin(120°) = 52 * (√3/2) ≈ 52 * 0.8660 ≈ 45.03
Therefore, v ≈ <-26, 45.03>
**3. Find the sum of vectors u and v**
* u + v =
* u + v = <31.72 + (-26), 14.79 + 45.03>
* u + v = <5.72, 59.82>
Therefore, u + v ≈ <5.72, 59.82>
Final Answer: The final answer is $\boxed{\langle 5.72, 59.82 \rangle}$
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