Solution Found!
(a) How do the components of a vector5 transform under a
Chapter 1, Problem 10P(choose chapter or problem)
(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
Questions & Answers
QUESTION:
(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
ANSWER:
a.)
Step 1 of 8
We have to find the transformation in the components of a vector under a translation of coordinates.
Translation of coordinates is given as
Consider a vector with components
and
.
The velocity is given by,
