(a) How do the components of a vector transform under a translation of coordinates (x = x, y = y ?? a, z = z, Fig. 1.16a)?

(b) How do the components of a vector transform under an inversion of coordinates (x = ?? x, Y = ?? y, z = ??z, Fig. 1.16b)?

(c) How does the cross product (1.13) of two vectors transform under inversion? [The cross-product of two vectors is properly called a pseudo vector because of this "anomalous" behavior.] Is the cross product of two pseudo vectors a vector, or a pseudo vector? Name two pseudo vector quantities in classical mechanics.

(d) How does the scalar triple product of three vectors transform under inversions? (Such an object is called a pseudoscalar.)

Transcribed Image Text:

XA IN a (a) y x N IN (b) y