Troubleshooting Vector Angles in Three Dimensions

In summary, vectors in three dimensions are quantities that have both magnitude and direction and are represented by directed line segments in a three-dimensional coordinate system. They are typically represented by three numbers or unit vectors in the x, y, and z directions. There is a difference between position vectors and displacement vectors, as the former represents a point's location relative to the origin while the latter represents a change in position. Vectors in three dimensions can be added or subtracted by adding or subtracting their corresponding components. The dot product of two vectors is a scalar quantity while the cross product is a vector perpendicular to the plane containing the two vectors.
  • #1
whynot314
76
0
ok so I am not sure how else to do this problem, my answers look similar to those in the book. where they have β=52.5 [itex]\alpha=121[/itex] [itex]\gamma=53.1[/itex], I feel like the book is wrong because i don't see any other way to solve this problem.

[URL=http://s1341.photobucket.com/user/nebula-314/media/20130523_174427_zpsda388c38.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130523_174427_zpsda388c38.jpg[/URL][/PLAIN]

Heres how I solved for the angles
[URL=http://s1341.photobucket.com/user/nebula-314/media/20130523_174442_zps9be6b8d1.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130523_174442_zps9be6b8d1.jpg[/URL][/PLAIN]
 
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  • #2
The gammas are the same so I am unsure where I went wrong.
 

1. What are vectors in three dimensions?

Vectors in three dimensions are quantities that have both magnitude and direction and are represented by directed line segments with a specific length and direction in a three-dimensional coordinate system.

2. How are vectors in three dimensions represented?

Vectors in three dimensions are typically represented by three numbers in a specific order, such as (x, y, z) or i + j + k where i, j, and k are unit vectors in the x, y, and z directions respectively.

3. What is the difference between a position vector and a displacement vector?

A position vector represents the location of a point in three-dimensional space relative to the origin, while a displacement vector represents the change in position of an object from one point to another.

4. How are vectors in three dimensions added and subtracted?

To add or subtract vectors in three dimensions, the corresponding components of the vectors are added or subtracted respectively. For example, (2, 3, 4) + (1, 2, 3) = (3, 5, 7) and (2, 3, 4) - (1, 2, 3) = (1, 1, 1).

5. What is the dot product and cross product of two vectors in three dimensions?

The dot product of two vectors in three dimensions is a scalar quantity that represents the product of the magnitudes of the vectors and the cosine of the angle between them. The cross product of two vectors is a vector that is perpendicular to the plane containing the two vectors and has a magnitude equal to the product of the magnitudes of the two vectors and the sine of the angle between them.

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