law of cosines for spherical triangle and cross product, Prob51Chap2

[PG1995]

Hi

Please have a look on the attachment and kindly help me with the queries there. This is the book I'm using; for the current problem go to page #36. Many thanks for your time.

Regards
PG

 

[Ratchit]

PG,

Q1: It is just you. Plug in C=A and D=C into the formula and see what you get.

Q2: On a unit radius sphere, the circumference of a great circle is 2∏. So a section of a great circle is the angle in radians. For instance, the angle of POQ is r.

The magnitude of the cross product of AxB is sin(r). The magnitude of the cross product of AxC is sin(q). The magnitude of the cross product of AxB and AxC is sin(P), and the vector of the cross product is A.

Q3: Each variable in the present equation is assigned the next variable in the sequence and a new equation is formed. So p is substituted for r, r is substituted for q, and q is substituted for p, etc. in a cyclic manner.

Ratch