Vectors and coordinates

Chandra image of LP 944-20 before flare and during flare. Credit: Marshall Space Flight Center/NASA.

This problem set is devoted to a variety of vector situations and coordinates for evaluation.

Evaluation

evaluation activity

Problem 1

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

If the x-axis is the longitude of the Greenwich meridian, and ax equals ay, then RA equals?

If ax equals ay equals az, then the declination is?

The value of a is given by?

Problem 2

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

for ax equals ay equals az

If the x-axis is the longitude of the Greenwich meridian, and the object is at ax and 2ay, then RA equals?

ax and 2ay and 3az, then the declination is?

The value of a is given by?

Problem 3

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

for ax equals ay equals az

If the x-axis is the longitude of the Greenwich meridian, and the object is at 3ax and 4ay, then RA equals?

3ax and 4ay and 5az, then the declination is?

The value of a is given by?

Problem 4

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), what are the right ascension, declination, and value of a:

for ax equals 2ay equals 3az

If the x-axis is the longitude of the Greenwich meridian, and the object is at 3ax and 4ay, then RA equals?

3ax and 4ay and 5az, then the declination is?

The value of a is given by?

Problem 5

An object has RA 10h 10m 10s Dec -20° 20' 20" and r = 23 lyrs.

What are ax, ay, and az?

What are ℓ and b?

What are the ecliptic longitude and latitude?

What are J1855 and B1855?

What are J2100 and B2100?

Problem 6

An object has coordinates: 125.678 -85.678 and r = 110 pc.

What are RA and Dec?

What are ax, ay, and az?

What are ℓ and b?

What are the ecliptic longitude and latitude?

What are J1800 and B1800?

What are J2075 and B2075?

Problem 7

For standard basis, or unit, vectors (i, j, k) and vector components of a (ax, ay, az), for ax equals 2ay equals 3az:

If the x-axis is the longitude of the Greenwich meridian, and the object is at a = 3ax and b = 4ay, then what is

a \times b?
a \cdot b?

Problem 8

Standard basis, or unit, vectors are (i, j, k) for vector components of a (ax, ay, az).

Let ax equal 3ay equal 4az.

What are

[5a_x, 6a_y, 7a_z] \cdot [5a_x, 6a_y, 7a_z]?

If a = [5a_x, 6a_y, 7a_z] and b = [8a_x, 9a_y, 10a_z], then

a \times b?

Research

Hypothesis:

  1. The square root of negative one is not needed in vector space.

Control groups

This is an image of a Lewis rat. Credit: Charles River Laboratories.

The findings demonstrate a statistically systematic change from the status quo or the control group.

“In the design of experiments, treatments [or special properties or characteristics] are applied to [or observed in] experimental units in the treatment group(s).[1] In comparative experiments, members of the complementary group, the control group, receive either no treatment or a standard treatment.[2]"[3]

Proof of concept

Def. a “short and/or incomplete realization of a certain method or idea to demonstrate its feasibility"[4] is called a proof of concept.

Def. evidence that demonstrates that a concept is possible is called proof of concept.

The proof-of-concept structure consists of

  1. background,
  2. procedures,
  3. findings, and
  4. interpretation.[5]

See also

References

  1. ↑ Klaus Hinkelmann, Oscar Kempthorne (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (2nd ed.). Wiley. ISBN 978-0-471-72756-9. http://books.google.com/?id=T3wWj2kVYZgC&printsec=frontcover.
  2. ↑ R. A. Bailey (2008). Design of comparative experiments. Cambridge University Press. ISBN 978-0-521-68357-9. http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521683579.
  3. ↑ "Treatment and control groups, In: Wikipedia". San Francisco, California: Wikimedia Foundation, Inc. May 18, 2012. Retrieved 2012-05-31.
  4. ↑ "proof of concept, In: Wiktionary". San Francisco, California: Wikimedia Foundation, Inc. November 10, 2012. Retrieved 2013-01-13.
  5. ↑ Ginger Lehrman and Ian B Hogue, Sarah Palmer, Cheryl Jennings, Celsa A Spina, Ann Wiegand, Alan L Landay, Robert W Coombs, Douglas D Richman, John W Mellors, John M Coffin, Ronald J Bosch, David M Margolis (August 13, 2005). "Depletion of latent HIV-1 infection in vivo: a proof-of-concept study". Lancet 366 (9485): 549-55. doi:10.1016/S0140-6736(05)67098-5. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1894952/. Retrieved 2012-05-09.

External links

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Educational level: this is a research resource.
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Subject classification: this is an astrophysics resource.
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