Vector manipulations and stuff

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The angle between the position vectors to the points (3,-4,0) and (-2,1,0) is calculated using the dot product, yielding an angle of 153.4°. The perpendicular vector is determined through the cross product, resulting in (0,0,-5) or (0,0,5). Direction cosines are derived by normalizing the components of the perpendicular vector, leading to values of 0, 0, and -1. The calculations and answers provided are confirmed to be correct. This demonstrates a solid understanding of vector manipulations.
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Homework Statement



Find the angle between the position vectors to the points (3,-4,0) and (-2,1,0) and find the direction cosines of a vector perpendicular to both.

Homework Equations



The Attempt at a Solution



You calculate the angle using the two definitions of the dot product (one that uses the magnitude of the vectors and the other that uses the components of the vectors). The answer is 153.4°. Is it right?

The perpendicular vector is the cross product of the two given vectors (the order of the vectors during the operation is immaterial, right?) and it is (0,0,-5) or (0,0,5). Is that right? The direction cosines are found by dividing the each component by the magnitude of the vector, right? So, using (0,0,-5), we get 0,0 and -1 for the direction cosines. Am I right?

I just need to know that my answers are correct, that's all! Please?
 
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Your answers are correct.
 
I agree with Kurtz. They are all correct. nice work
 

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