Both by Pythagorean theorem and dot product approaches, we find that the magnitude of the vector u = <4, 7> is equal to √65.
Vectors are characterized by two elements: Magnitude and direction, the magnitude is a scalar that represents the "length" of the vector, while the direction indicate the "orientation" of the vector. There are two methods to find the magnitude of the vector u:
Method 1 - Pythagorean theorem
u = <4, 7>
u = √(4² + 7²)
u = √65
Method 2 - Dot product
u = <4, 7>
u = √(u • u)
u = √[(4, 7) • (4, 7)]
u = √(4² + 7²)
u = √65
Both by Pythagorean theorem and dot product approaches, we find that the magnitude of the vector u = <4, 7> is equal to √65.
To learn more on vectors: https://brainly.com/question/13322477
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