Simple linear algebra question (test in a few hours)

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SUMMARY

The discussion centers on the interpretation of a parametrized line in three-dimensional space, specifically the equations x - 1 = 4t, y - 5 = 3t, and z - 2 = 7t. The vector <4, 3, 7> is confirmed as a direction vector parallel to the line, contradicting the initial claim that it is a normal vector. The consensus is that the vector represents the direction of the line, aligning with standard linear algebra principles.

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  • Understanding of parametrized lines in three-dimensional space
  • Knowledge of vector representation and properties
  • Familiarity with linear algebra concepts
  • Ability to differentiate between normal and direction vectors
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my book says that if you have a parametrized line in 3 dimensions
i.e.:
x - 1 = 4t
y - 5 = 3t
z - 2 = 7t,

the vector <4, 3, 7> (coefficients of t) is a vector parallel to that line.

My notes clearely say that the vector <4, 3, 7> is a normal vector to the parametrized line.

Which one is right?

Thanks.
 
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It should be parallel.

- harsh
 
Ok thanks. That's what I thought...I should drink some caffiene before I go to class and take notes. :smile:
 

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