Physics quiz question: direction of vector, given components

Physics 205A Quiz 3, fall semester 2012
Cuesta College, San Luis Obispo, CA

Of the three vectors P, Q, and R shown, the direction of vector R is __________, as measured counterclockwise from the +x axis.
(A) 108°.
(B) 162°.
(C) 198°.
(D) 252°.

Correct answer (highlight to unhide): (C)

Many calculators do not properly calculate the angle of a vector counterclockwise from the +x axis, instead calculating an angle θ for the related vector in the first quadrant (by dropping ± signs from the R_x and R_y components in the arctangent operation. Thus this "first quadrant angle" θ is:

θ = Arctan|R_y/R_x| = Arctan|(6 units)/(2 units)| = +18°.

However, since we know that the vector R must be in the third quadrant, then we will need to add this "first quadrant angle" θ to 180° such that the direction of R measured counterclockwise from the +x axis is:

180° + 18° = 198°.

For the cases of vectors in other quadrants, if the vector truly lies in the first quadrant, then its direction is the same as the "first quadrant angle" θ. If the vector lies in the second quadrant, then its direction is the "first quadrant angle" θ subtracted from 180°. If the vector lies in the fourth quadrant, then its direction is the "first quadrant angle" θ subtracted from 360°.

Sections 70854, 70855
Exam code: quiz03sQr7
(A) : 8 student
(B) : 6 students
(C) : 41 students
(D) : 1 student

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.56