(a) How do the components of a vector5 transform under a translation of coordinates Fig...

(a) How do the components of a vector⁵ transform under a translation of coordinates Fig. 1.16a)?

(b) How do the components of a vector transform under an inversion of coordinates Fig. 1.16b)?

(c) How do the components of a cross product (Eq. 1.13) transform under inversion? [The cross-product of two vectors is properly called a pseudovector because of this “anomalous” behavior.] Is the cross product of two pseudovectors a vector, or a pseudovector? Name two pseudovector quantities in classical mechanics.

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

Reference equation 1.13