Math Problem Statement
If \(\vec{v} = (1, -2, 2, 4)\), find \(|\vec{v}|\).
Solution
To find for the vector , we calculate the magnitude of using the formula:
where , , , and .
Calculating step-by-step:
Summing these values:
Thus, .
Would you like further details on the process or have any questions?
Here are some related questions that could expand your understanding:
- How do you find the magnitude of a vector in three-dimensional space?
- What are some real-world applications of finding the magnitude of a vector?
- How does the concept of vector magnitude apply in physics?
- Can vectors have negative magnitudes, and why or why not?
- How would the magnitude change if one of the vector components was zero?
Tip: Remember that the magnitude of a vector is always a non-negative value.
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Math Problem Analysis
Mathematical Concepts
Vector Magnitude
Euclidean Distance
Linear Algebra
Formulas
Magnitude of a vector formula: |\vec{v}| = \sqrt{x_1^2 + x_2^2 + x_3^2 + x_4^2}
Theorems
Pythagorean Theorem (for finding distances in multidimensional space)
Suitable Grade Level
Grade 10-12