Find a unit vector in the direction of (2,4)

In this video, we will learn how to find a unit vector in the direction of a given vector, specifically 2,4. We will also go through the process of rationalizing the result.

To find the unit vector in the direction of 2,4, we use the formula u=v/||v||, where u is the unit vector, v is the given vector, and ||v|| is the magnitude of v. Since we already have v, we just need to compute the magnitude of 2,4, which is found using the Pythagorean theorem.

After simplifying, we get 2√5 as the magnitude of v. From there, we can form the unit vector u by dividing v by ||v||. Rationalizing the denominator, we end up with 2√5/5 as the final answer.

It's important to note that whenever we have a square root of a value multiplied by the square root of the same value, we can use exponential notation to simplify it.

If you're looking to learn how to find unit vectors or just need a refresher, this video is perfect for you! Make sure to like and subscribe for more math content.

🔎Keywords unit vector, magnitude, Pythagorean theorem, rationalizing, exponential notation.

📋Common Questions

1️⃣ What is a unit vector?
A unit vector is a vector that has a magnitude of 1. It is found by dividing a given vector by its magnitude.

2️⃣ What is the magnitude of a vector?
The magnitude of a vector is the length of the vector. It is found using the Pythagorean theorem.

3️⃣ What is the Pythagorean theorem?
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

4️⃣ What is rationalizing the denominator?
Rationalizing the denominator is the process of removing any square roots from the denominator of a fraction.

5️⃣ What is exponential notation?
Exponential notation is a way to write a number as a base raised to a power. For example, 2^3 means 2 raised to the power of 3.

6️⃣ How do you find a unit vector?
To find a unit vector, divide a given vector by its magnitude.

7️⃣ How do you find the magnitude of a vector?
To find the magnitude of a vector, use the Pythagorean theorem.

8️⃣ What is a square root?
A square root is a value that, when multiplied by itself, gives the original value.

9️⃣ What is a denominator?
The denominator is the bottom part of a fraction that represents the total number of parts that make up the whole.

🔟 What is a numerator?
The numerator is the top part of a fraction that represents the number of parts that we are interested in.

1️⃣1️⃣ What is a radical sign?
A radical sign is a symbol used to indicate the square root of a value.

1️⃣2️⃣ What is a fraction?
A fraction is a numerical quantity that represents a part of a whole or a ratio between two quantities.

1️⃣3️⃣ What is a square?
A square is a four-sided figure with all sides equal in length and all angles right angles.

1️⃣4️⃣ What is an exponent?
An exponent is a mathematical notation that indicates the number of times
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