Answer: |b+c| ≈ 28.01
Explanation:
To find the magnitude of the vector sum of b and c, we can use the Law of Cosines.
First, let's find the dot product of b and c:
b · c = ||b|| ||c|| cosθ
where θ is the angle between b and c.
Substituting the given values, we get:
b · c = (12)(18) cos 38°
b · c ≈ 193.92
Next, we can use the Law of Cosines to find |b+c|:
|b+c|² = ||b||² + ||c||² + 2||b||||c||cosθ
Substituting the given values and the dot product we just found, we get:
|b+c|² = (12)² + (18)² + 2(12)(18)cos 38°
|b+c|² ≈ 784.65