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

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

Step 1: Identify the vector you want to find the unit vector for. In this case, the vector is (3, 4).
Step 2: Calculate the magnitude of the vector. Use the formula: Magnitude = √(x^2 + y^2), where x and y are the components of the vector.
Step 3: Substitute the values into the formula: Magnitude = √(3^2 + 4^2).
Step 4: Calculate 3^2, which is 9, and 4^2, which is 16.
Step 5: Add the results: 9 + 16 = 25.
Step 6: Take the square root of 25: √25 = 5. This is the magnitude of the vector.
Step 7: To find the unit vector, divide each component of the original vector by the magnitude.
Step 8: Divide the x-component: 3 / 5 = 0.6.
Step 9: Divide the y-component: 4 / 5 = 0.8.
Step 10: Write the unit vector as (0.6, 0.8).

Unit Vector – A unit vector is a vector that has a magnitude of 1 and indicates direction.
Magnitude of a Vector – The magnitude of a vector is calculated using the Pythagorean theorem, which involves squaring the components, summing them, and taking the square root.
Normalization – To find a unit vector, divide each component of the vector by its magnitude.