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Nevermore
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How would I find the direction vector of a line given in the form ax + by + cz +d =0?
Thankyou.
Thankyou.
Finding the Direction Vector of a Line: Tips and Tricks
In summary, to find the direction vector of a line given in the form ax + by + c = 0, you can use the slope of the line, which is represented by (1,m) where m is the slope. This information can be helpful in finding the direction of the line. The conversation also includes apologies for mistaking an equation of a plane for a line and gratitude for the question being asked.
- #2
TD
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I see an equation of a plane, not a line.
- #3
Nevermore
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Damn, sorry, got carried away with my letters. I meant ax + by +c = 0. Sorry about that...
- #4
TD
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For a line, (1,m) is always a directional vector where m is the slope. Can you find the slope?Nevermore said:
- #5
Nevermore
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Yeah - I thought it would be something simple like that. Thanks for your help.
- #6
TD
Homework Helper
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You're welcome 
- #7
SirAllan
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Thanks for asking that Q, it helped me too
- #8
Defennder
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I don't think there's a need to thank someone who started a thread two years ago and have not posted since.
- #9
SirAllan
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LORL... Thanks for pointing that out. ( At least you still logon)
What is the definition of a direction vector of a line?
A direction vector of a line is a mathematical representation of the direction and slope of a line in two or three-dimensional space. It is typically represented by a vector with two or three components, depending on the dimension of the space.
How is a direction vector of a line determined?
A direction vector of a line can be determined by finding the difference between any two points on the line and representing that difference as a vector. This vector will have the same direction as the line and can be expressed in terms of the x, y, and z components.
What is the significance of a direction vector of a line?
A direction vector of a line is important because it provides information about the slope and direction of the line. This information can be used to calculate the angle between two lines, determine if two lines are parallel or perpendicular, and find the shortest distance between two lines.
How is the direction vector of a line related to its equation?
The direction vector of a line is directly related to its equation. In two-dimensional space, the direction vector is the slope of the line, which is represented by the coefficient of the x term in the line's equation. In three-dimensional space, the direction vector is a vector that is parallel to the line and is represented by the coefficients of the x, y, and z terms in the line's equation.
Can the direction vector of a line be negative?
Yes, the direction vector of a line can be negative. In two-dimensional space, a negative direction vector indicates that the line is sloping downwards from left to right. In three-dimensional space, a negative direction vector indicates that the line is sloping downwards in that particular direction.
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