If A = 5i + 12j, what is the unit vector in the direction of A? (2021)

If A = 5i + 12j, what is the unit vector in the direction of A? (2021)

Step 1: Identify the vector A, which is given as A = 5i + 12j.
Step 2: Calculate the magnitude (length) of vector A, denoted as |A|. Use 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| = √(5^2 + 12^2).
Step 4: Calculate 5^2, which is 25, and 12^2, which is 144.
Step 5: Add these two results together: 25 + 144 = 169.
Step 6: Take the square root of 169 to find |A|: √169 = 13.
Step 7: Now, to find the unit vector in the direction of A, use the formula: Unit vector = A / |A|.
Step 8: Substitute A and |A| into the formula: Unit vector = (5i + 12j) / 13.
Step 9: Divide each component of the vector by 13: (5/13)i + (12/13)j.
Step 10: The final result is the unit vector in the direction of A: (5/13)i + (12/13)j.

Vector Representation – Understanding how to represent vectors in terms of their components (i and j) and how to manipulate them.
Magnitude of a Vector – Calculating the magnitude of a vector using the Pythagorean theorem.
Unit Vectors – Finding a unit vector by dividing a vector by its magnitude.