Vectors and coordinates

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

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

Problem 1

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

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

If a_x equals a_y equals a_z, 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 (a_x, a_y, a_z), what are the right ascension, declination, and value of a:

for a_x equals a_y equals a_z

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

a_x and 2a_y and 3a_z, 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 (a_x, a_y, a_z), what are the right ascension, declination, and value of a:

for a_x equals a_y equals a_z

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

3a_x and 4a_y and 5a_z, 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 (a_x, a_y, a_z), what are the right ascension, declination, and value of a:

for a_x equals 2a_y equals 3a_z

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

3a_x and 4a_y and 5a_z, then the declination is?

The value of a is given by?

Problem 5

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

What are a_x, a_y, and a_z?

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 a_x, a_y, and a_z?

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 (a_x, a_y, a_z), for a_x equals 2a_y equals 3a_z:

If the x-axis is the longitude of the Greenwich meridian, and the object is at a = 3a_x and b = 4a_y, 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 (a_x, a_y, a_z).

Let a_x equal 3a_y equal 4a_z.

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

$a\times b?$

Hypotheses

Main resource: Hypotheses

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

See also

• Angular momentum and energy
• Column densities
• Cosmic circuits
• Energy phantoms
• Furlongs per fortnight
• Planck's equation
• Radiation astronomy/Problem set
• Radiation dosage
• Radiation mathematics/Problem set
• Spectrographs
• Star jumping
• Synchrotron radiation problem set
• Telescopes and cameras
• Unknown coordinate systems
• Unusual units
• Vectors and coordinates

External links

• International Astronomical Union
• NASA/IPAC Extragalactic Database - NED
• NASA's National Space Science Data Center
• Office of Scientific & Technical Information
• The SAO/NASA Astrophysics Data System
• Scirus for scientific information only advanced search
• SDSS Quick Look tool: SkyServer
• SIMBAD Astronomical Database
• SIMBAD Web interface, Harvard alternate
• Spacecraft Query at NASA
• Universal coordinate converter

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