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

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

Options:

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

Solution:

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

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

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

Step 1: Identify the vector given, which is (4, 3).
Step 2: Calculate the magnitude of the vector using the formula: magnitude = √(x^2 + y^2). Here, x = 4 and y = 3.
Step 3: Substitute the values into the formula: magnitude = √(4^2 + 3^2) = √(16 + 9) = √25 = 5.
Step 4: To find the unit vector, divide each component of the vector by the magnitude. The unit vector is (4/magnitude, 3/magnitude).
Step 5: Substitute the magnitude into the unit vector formula: unit vector = (4/5, 3/5).

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