Both by Pythagorean theorem and dot product approaches, we find that the magnitude of the vector <u>u</u> = <4, 7> is equal to √65.
<h3>What is the magnitude of a vector?</h3>
Vectors are characterized by two elements: Magnitude and direction, the magnitude is a scalar that represents the <em>"length"</em> of the vector, while the direction indicate the <em>"orientation"</em> of the vector. There are two methods to find the magnitude of the vector u:
Method 1 - Pythagorean theorem
<u>u</u> = <4, 7>
u = √(4² + 7²)
u = √65
Method 2 - Dot product
<u>u</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>u</u> = <4, 7> is equal to √65.
To learn more on vectors: brainly.com/question/13322477
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Answer:
62.182°
Step-by-step explanation:
Using <em>cos</em> and <em>sin</em> you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.