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

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

Options:

Correct Answer: (0.6, 0.8)

Solution:

Unit vector = v / |v| = (3, 4) / 5 = (0.6, 0.8)

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

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

Step 1: Identify the vector v, which is given as (3, 4).
Step 2: Calculate the magnitude (length) of the vector v using the formula |v| = √(x^2 + y^2), where x = 3 and y = 4.
Step 3: Substitute the values into the formula: |v| = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.
Step 4: To find the unit vector, divide each component of the vector v by its magnitude: unit vector = v / |v|.
Step 5: Perform the division: unit vector = (3/5, 4/5).
Step 6: Simplify the fractions: unit vector = (0.6, 0.8).

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