1st year linear algebra question

In summary, to find the equation of a line through P that is parallel to the line through Q and R, you need to find the direction vector by subtracting the coordinates of Q and R, and then add that vector to P to find another point on the line. This point and the direction vector can then be used to write the equation in point-slope form.
  • #1
michaelgtozer
8
1
given P(-1,1,2), Q(-3,0,4), R(3,2,1), find an equation of the line through P that is parallel to the line through Q and R.

All the words after the given three points really confuse me and I just need some help on where to start to tackle this problem.

Thanks
 
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  • #2
Geometrically, you need to find a line going through P. But not just any line will do - it's got to be parallel to another line. Which line does it need to be parallel to? The one going through Q and R. So, Step One would be to find the line going through Q and R.
 
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Likes Greg Bernhardt
  • #3
since 2 days have passed, maybe more detailed help is warranted. basic facts: point - point = vector parallel to the line through the two points. point + vector = another point on the line through the first point and having the given direction vector.

In general you can subtract 2 points and get a direction vector; and you can add a vector to a point to get another point on the line through the given point and parallel to the given vector.oops a year has passed!
 
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Related to 1st year linear algebra question

1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It involves the study of vectors, matrices, and their operations, as well as systems of linear equations and their solutions.

2. What topics are typically covered in a 1st year linear algebra course?

In a 1st year linear algebra course, you will typically cover topics such as vector operations, matrix operations, systems of linear equations, determinants, eigenvalues and eigenvectors, and applications of linear algebra in areas such as geometry, physics, and computer science.

3. How is linear algebra used in real life?

Linear algebra is used in various fields such as physics, engineering, economics, and computer science. It is used to solve problems involving systems of linear equations, to model and analyze relationships between variables, and to perform operations on large sets of data.

4. What skills are necessary for success in a 1st year linear algebra course?

To succeed in a 1st year linear algebra course, it is important to have a solid understanding of basic algebra and geometry. You should also have good problem-solving skills, the ability to think abstractly, and a strong foundation in mathematical concepts and logic.

5. How can I prepare for a 1st year linear algebra course?

To prepare for a 1st year linear algebra course, you can review your algebra and geometry skills, practice solving systems of linear equations, and familiarize yourself with basic matrix operations. You can also read ahead in your textbook or look for online resources and practice problems to get a head start on the course material.

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