Final answer:
The direction angle for the vector -8i + 7j is found using the arctan function. Since the vector lies in the second quadrant, the angle is approximately 138.81 degrees. The correct answer is option b) 138.81 degrees.
Step-by-step explanation:
To find the direction angle for the vector -8i + 7j, we use the tangent function which relates the x and y components of the vector. The tangent of the direction angle θ is equal to the y-component of the vector divided by the x-component of the vector. Thus, we have:
tan(θ) = 7 / -8
Since the vector is in the second quadrant (negative x, positive y), the direction angle θ will be between 90° and 180°. Using the arctan function to find the angle, we get:
θ = arctan(7 / -8)
θ = arctan(-0.875)
θ = approximately 138.81°
Therefore, the correct answer is b) 138.81 degrees.