Final answer:
The direction angle of vector v with a direction of (-3, 21) is 98.1°, as it lies in the second quadrant where the angles are determined by adding 180° to the tangent inverse result.
Therefore, the correct answer is: option "98.1°"
Step-by-step explanation:
To find the direction angle of vector v with a direction of (-3, 21), we need to calculate the angle the vector makes with the positive x-axis.
Since the vector has a negative x-component (-3) and a positive y-component (21), it lies in the second quadrant. The angle θ in the second quadrant can be found using the tangent inverse function:
tan(θ) = y / x
tan(θ) = 21 / -3
= -7
θ = tan⁻¹(-7)
The calculator will give a negative angle because the tangent of angles in the second quadrant is negative.
However, the correct angle is found by adding 180° to the calculator's result since angles are positive in the counter-clockwise direction.
Assuming the calculator's inverse tangent function gives us an angle of approximately -81.9°, adding 180°:
θ = -81.9° + 180°
= 98.1°
Therefore, the direction angle of vector v is 98.1°.