What is the unit vector in the direction of (3, 4, 0)?

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Question: What is the unit vector in the direction of (3, 4, 0)?

Options:

Correct Answer: (0.6, 0.8, 0)

Solution:

Unit vector = (3, 4, 0) / √(3^2 + 4^2) = (3, 4, 0) / 5 = (0.6, 0.8, 0).

What is the unit vector in the direction of (3, 4, 0)?

What is the unit vector in the direction of (3, 4, 0)?

Step 1: Identify the vector given, which is (3, 4, 0).
Step 2: Calculate the magnitude (length) of the vector using the formula √(x^2 + y^2 + z^2). Here, x = 3, y = 4, and z = 0.
Step 3: Calculate x^2, which is 3^2 = 9.
Step 4: Calculate y^2, which is 4^2 = 16.
Step 5: Calculate z^2, which is 0^2 = 0.
Step 6: Add these values together: 9 + 16 + 0 = 25.
Step 7: Take the square root of 25 to find the magnitude: √25 = 5.
Step 8: To find the unit vector, divide each component of the original vector (3, 4, 0) by the magnitude (5).
Step 9: Calculate the new x component: 3 / 5 = 0.6.
Step 10: Calculate the new y component: 4 / 5 = 0.8.
Step 11: Calculate the new z component: 0 / 5 = 0.
Step 12: Combine these results to get the unit vector: (0.6, 0.8, 0).

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