Find the unit vector in the direction of the vector (4, 3).

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Question: Find the unit vector in the direction of the vector (4, 3).

Options:

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

Solution:

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

Find the unit vector in the direction of the vector (4, 3).

Find the unit vector in the direction of the vector (4, 3).

Step 1: Identify the given vector, which is (4, 3).
Step 2: Calculate the magnitude (length) of the vector using the formula: √(x^2 + y^2), where x and y are the components of the vector.
Step 3: Substitute the values into the formula: √(4^2 + 3^2).
Step 4: Calculate 4^2, which is 16, and 3^2, which is 9.
Step 5: Add the results: 16 + 9 = 25.
Step 6: Take the square root of 25, which is 5. This is the magnitude of the vector.
Step 7: To find the unit vector, divide each component of the vector (4, 3) by the magnitude (5).
Step 8: Calculate the new components: 4/5 and 3/5.
Step 9: Write the unit vector as (4/5, 3/5).

Unit Vector – A unit vector is a vector that has a magnitude of 1 and indicates direction.
Magnitude of a Vector – The magnitude of a vector (x, y) is calculated using the formula √(x² + y²).
Vector Normalization – To find a unit vector in the direction of a given vector, divide the vector by its magnitude.