Question
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
A. 98.1
B. 261.9
C. 81.9
D. 278.1
Answers
GPT 3.5
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.
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.