Rotation as a vector
No, no, please, Zapboy, don't cavil with words.
From "Advanced Enginering Maths" by KREYSZIG, " ... a vector is fixed in length and direction ..."
Yes, there exist sliding and bound vectors too. (See KREYSZIG). That merely moves the point of application. It does not allow the length, or direction of a vector to alter.
Thus the VECTOR itself does not rotate, as Zapboy (and Serway & Beichner) imply.
I repeat, a vector can represent (symbolise) rotation ONLY if it represents angular velocity or angular acceleration. It CANNOT represent angular displacement. Thus the word ROTATION is too shoddy and imprecise for use by professional engineers, and should only be used circumspectly when talking to "lay" people.
A PHASOR, on the other hand, is a line segment that rotates about its' tail, while its' head, with the addition of some trig., represents the generation of a sinusoid. Its length represents the magnitude of the sinusoid, and its angle (wrt X axis) represents phase, and its' angular velocity represents angular frequency, in rad/sec, convertible to Hertz.
A PHASOR is not a VECTOR, and here I will gladly contest my 30 years of tertiary lecturing, in Electrical Engineering, against the cited physics text.
A PHASOR is a trivial graphical device used to represent s-plane functions, which anyway are BETTER represented by Laplacian algebraic functions. See for example, CH.9 of "Network Analysis", M.E. van VALKENBURG.