Find the unit vector in the direction of the vector (3, 4, 0).

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Question: Find the unit vector in the direction of the vector (3, 4, 0).

Options:

Correct Answer: (0.6, 0.8, 0)

Solution:

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

Find the unit vector in the direction of the vector (3, 4, 0).

Find the unit vector in the direction of the vector (3, 4, 0).

Step 1: Identify the given vector, which is (3, 4, 0).
Step 2: Calculate the magnitude of the vector using the formula: Magnitude = √(x^2 + y^2 + z^2). Here, x = 3, y = 4, and z = 0.
Step 3: Substitute the values into the formula: Magnitude = √(3^2 + 4^2 + 0^2).
Step 4: Calculate 3^2 = 9 and 4^2 = 16. So, Magnitude = √(9 + 16 + 0) = √25.
Step 5: Find the square root of 25, which is 5. So, the magnitude of the vector is 5.
Step 6: To find the unit vector, divide each component of the original vector by the magnitude. The unit vector = (3/5, 4/5, 0/5).
Step 7: Calculate each component: 3/5 = 0.6, 4/5 = 0.8, and 0/5 = 0.
Step 8: Write the unit vector as (0.6, 0.8, 0).

Magnitude of a Vector – The magnitude of a vector is calculated using the formula √(x^2 + y^2 + z^2) for a 3D vector.
Unit Vector – A unit vector is a vector that has a magnitude of 1 and is found by dividing each component of the vector by its magnitude.