What is the unit vector in the direction of (3, 4)?

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Question: What is the unit vector in the direction of (3, 4)?

Options:

Correct Answer: (3/5, 4/5)

Solution:

Unit vector = (3, 4) / √(3^2 + 4^2) = (3/5, 4/5).

What is the unit vector in the direction of (3, 4)?

What is the unit vector in the direction of (3, 4)?

Step 1: Identify the vector you want to find the unit vector for. In this case, the vector is (3, 4).
Step 2: Calculate the magnitude (length) of the vector. Use the formula: √(x^2 + y^2), where x and y are the components of the vector.
Step 3: Substitute the values into the formula: √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Step 4: Divide each component of the vector by the magnitude to find the unit vector. This means you will calculate (3/5, 4/5).
Step 5: The result (3/5, 4/5) is the unit vector in the direction of (3, 4).

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