Find the unit vector in the direction of the vector (6, 8).

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Question: Find the unit vector in the direction of the vector (6, 8).

Options:

Correct Answer: (0.6, 0.8)

Solution:

Magnitude = √(6^2 + 8^2) = √(36 + 64) = √100 = 10. Unit vector = (6/10, 8/10) = (0.6, 0.8).

Find the unit vector in the direction of the vector (6, 8).

Find the unit vector in the direction of the vector (6, 8).

Step 1: Identify the vector you want to find the unit vector for. In this case, the vector is (6, 8).
Step 2: Calculate the magnitude of the vector. Use the formula: Magnitude = √(x^2 + y^2), where x and y are the components of the vector.
Step 3: Substitute the values into the formula: Magnitude = √(6^2 + 8^2).
Step 4: Calculate 6^2, which is 36, and 8^2, which is 64.
Step 5: Add the results: 36 + 64 = 100.
Step 6: Take the square root of 100 to find the magnitude: √100 = 10.
Step 7: To find the unit vector, divide each component of the original vector by the magnitude. For the x-component: 6 / 10 = 0.6.
Step 8: For the y-component: 8 / 10 = 0.8.
Step 9: Combine the results to get the unit vector: (0.6, 0.8).

Vector Magnitude – Understanding how to calculate the magnitude of a vector using the Pythagorean theorem.
Unit Vector – Knowing how to find a unit vector by dividing each component of the vector by its magnitude.