Question
Find the magnitude of the vector \( <-4,-6> \). 6.4 10 8 7.2
Ask by Romero Pena. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The magnitude of the vector <-4, -6> is 7.2.
Solution
To find the magnitude of the vector <-4, -6>, use the formula for the magnitude of a vector:
Magnitude = √(x² + y²)
Substitute the components:
Magnitude = √((-4)² + (-6)²)
= √(16 + 36)
= √52
We can simplify √52:
√52 = √(4×13) = 2√13 ≈ 7.2
Thus, the magnitude of the vector is 7.2.
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Simplify this solution Beyond the Answer
To find the magnitude of the vector \( <-4, -6> \), you can use the formula for the magnitude of a vector \( \|v\| = \sqrt{x^2 + y^2} \). Substituting the values, we calculate \( \|v\| = \sqrt{(-4)^2 + (-6)^2} = \sqrt{16 + 36} = \sqrt{52} \approx 7.2 \). So, the correct answer is 7.2! Keep in mind that the magnitude of a vector represents its length in space and is always a non-negative value.
