How can I solve for beta and gamma in a cartesian vector addition problem?

In summary, addition of cartesian vectors is a mathematical operation where the components of two or more vectors are added together to produce a single vector. Cartesian vectors, also known as rectangular vectors, are quantities with magnitude and direction represented by coordinates in a Cartesian coordinate system. To add cartesian vectors, one must identify and add the corresponding components and use trigonometry to find the magnitude and direction of the resulting vector. The main difference between scalar and vector addition is that scalar addition yields a single quantity, while vector addition yields a single vector. Additionally, cartesian vectors can be added in any order due to the commutative property of vector addition.
  • #1
whynot314
76
0
I am having a really tough time trying to solve this particular problem I can find alpha easily 139 degrees which is correct. However when I go to try and solve for beta or gamma I get this huge mess and I am unable to solve for either one, Please help me I know I am overlooking something but I don't know what it is.

[URL=http://s1341.photobucket.com/user/nebula-314/media/20130623_203154_zpsc06ba2e7.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130623_203154_zpsc06ba2e7.jpg[/URL][/PLAIN]


20130623_204207_zps5704c549.jpg
 
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  • #2
You need to show your reasoning, not just a sheet full of symbols and numbers.
 

What is addition of cartesian vectors?

Addition of cartesian vectors is a mathematical operation that combines two or more vectors to produce a single vector. It involves adding the corresponding components of each vector to obtain the components of the resulting vector.

What are cartesian vectors?

Cartesian vectors, also known as rectangular vectors, are mathematical quantities that have both magnitude and direction. They are represented by a set of coordinates in a Cartesian coordinate system.

How do you add cartesian vectors?

To add cartesian vectors, you must first identify the components of each vector in terms of their magnitude and direction. Then, add the corresponding components together to obtain the components of the resulting vector. Finally, use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the resulting vector.

What is the difference between scalar and vector addition?

Scalar addition involves adding two or more quantities that have magnitude but no direction, while vector addition involves adding two or more quantities that have both magnitude and direction. Scalar addition results in a single quantity, whereas vector addition results in a single vector.

Can cartesian vectors be added in any order?

Yes, cartesian vectors can be added in any order. The result will be the same regardless of the order in which the vectors are added. This is known as the commutative property of vector addition.

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