Answer:
To find the direction angle of the vector 13i + 15j, we can use trigonometry.
1. First, let's determine the magnitude (or length) of the vector.
The magnitude of a vector v = xi + yj is given by √(x² + y²).
In this case, the magnitude of 13i + 15j is √(13² + 15²) = √(169 + 225) = √394.
2. Next, let's find the direction angle θ using the formula:
θ = arctan(y/x), where x and y are the coefficients of i and j respectively.
In this case, x = 13 and y = 15. Therefore, θ = arctan(15/13).
3. To find the direction angle in degrees, we can use a calculator or trigonometric table to evaluate the arctan(15/13).
Using a calculator, we find that arctan(15/13) is approximately 48.37 degrees.
Therefore, the direction angle of the vector 13i + 15j is approximately 48.37 degrees.
Explanation: