Vector v has a direction of (-3, 21). Find the direction angle for v.
A. 98.1
B. 261.9
C. 81.9
D. 278.1
To find the direction angle for vector v, we need to use the formula:
θ = arctan(y/x)
Given that the direction of vector v is (-3, 21), we have x = -3 and y = 21.
Therefore, θ = arctan(21/-3) = arctan(-7) ≈ -81.87°
However, the direction angle is typically given as a positive angle. Since (-3, 21) lies in the second quadrant, we add 180° to get the direction angle in the range of [0°, 360°]:
θ = -81.87° + 180° = 98.13°
So, the direction angle for vector v is approximately 98.1°.
The answer is A. 98.1.