Short Answer 
To calculate the magnitude of the vector ∣∣ c . u ∣∣ with u = (5, -12) and c = -3, we use the dot product property resulting in ∣∣ c . u ∣∣ = |−3| * √((5)² + (−12)²), which simplifies to 39 after step-by-step calculations.
Step 1: Understand Given Values
To calculate the value of ∣∣ c . u ∣∣, start with the known values:
- u = (5, -12)
- c = -3
These values will be plugged into the formula to determine the magnitude of the resulting vector.
Step 2: Apply the Dot Product Property
Use the dot product property to find the magnitude of the vector:
- Calculate ∣∣ c . u ∣∣ using the formula: ∣∣ c . u ∣∣ = ∣∣ c ∣∣ * ∣∣ u ∣∣
- Substituting the given values, we get ∣∣ −3 (5, -12) ∣∣ = |−3| * √((5)² + (−12)²)
This simplifies further as we compute the magnitude of vector u.
Step 3: Final Calculations
Now, complete the calculations step-by-step:
- Calculate ∣∣ c . u ∣∣ = 3 * √(25 + 144)
- Thus, ∣∣ c . u ∣∣ = 3 * √169
- Finally, ∣∣ c . u ∣∣ = 3 * 13 = 39
Therefore, the correct option is C), confirming the accuracy of the computation.