The unit vector in the direction of vector A = 6i - 8j is:

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Question: The unit vector in the direction of vector A = 6i - 8j is:

Options:

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

Solution:

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

The unit vector in the direction of vector A = 6i - 8j is:

The unit vector in the direction of vector A = 6i - 8j is:

Step 1: Identify the vector A, which is given as A = 6i - 8j.
Step 2: Calculate the magnitude (length) of vector A using the formula |A| = √(x^2 + y^2), where x and y are the coefficients of i and j respectively.
Step 3: Substitute the values into the formula: |A| = √(6^2 + (-8)^2).
Step 4: Calculate 6^2 = 36 and (-8)^2 = 64.
Step 5: Add the results: 36 + 64 = 100.
Step 6: Take the square root: |A| = √100 = 10.
Step 7: Now, find the unit vector by dividing vector A by its magnitude: Unit vector = A / |A|.
Step 8: Substitute the values: Unit vector = (6i - 8j) / 10.
Step 9: Simplify the expression: Unit vector = (6/10)i - (8/10)j.
Step 10: Reduce the fractions: Unit vector = (3/5)i - (4/5)j.

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