Find the unit vector in the direction of vector A = 6i - 8j.

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Question: Find the unit vector in the direction of vector A = 6i - 8j.

Options:

Correct Answer: 3/5 i - 4/5 j

Solution:

Magnitude |A| = √(6^2 + (-8)^2) = √(36 + 64) = 10. Unit vector = (6/10)i + (-8/10)j = (3/5)i - (4/5)j.

Find the unit vector in the direction of vector A = 6i - 8j.

Find the unit vector in the direction of vector A = 6i - 8j.

Step 1: Identify the vector A. Here, A = 6i - 8j.
Step 2: Calculate the magnitude of vector A using the formula |A| = √(x^2 + y^2), where x and y are the coefficients of i and j.
Step 3: Substitute the values into the formula: |A| = √(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: |A| = √100 = 10.
Step 7: To find the unit vector, divide each component of vector A by its magnitude. The unit vector = (6/10)i + (-8/10)j.
Step 8: Simplify the fractions: (6/10) = (3/5) and (-8/10) = (-4/5).
Step 9: Write the unit vector in the final form: Unit vector = (3/5)i - (4/5)j.

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.