What is the unit vector in the direction of vector A = 4i + 3j?

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Question: What is the unit vector in the direction of vector A = 4i + 3j?

Options:

Correct Answer: (4/5)i + (3/5)j

Solution:

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

What is the unit vector in the direction of vector A = 4i + 3j?

What is the unit vector in the direction of vector A = 4i + 3j?

Step 1: Identify the vector A. In this case, A = 4i + 3j.
Step 2: Calculate the magnitude (length) of vector A. Use the formula |A| = √(4^2 + 3^2).
Step 3: Calculate 4^2, which is 16, and 3^2, which is 9.
Step 4: Add the results from Step 3: 16 + 9 = 25.
Step 5: Take the square root of 25 to find |A|. √25 = 5.
Step 6: Now, find the unit vector by dividing vector A by its magnitude: Unit vector = A / |A|.
Step 7: Substitute A and |A| into the formula: Unit vector = (4i + 3j) / 5.
Step 8: Simplify the expression: Unit vector = (4/5)i + (3/5)j.

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