- #1
lockedup
- 67
- 0
Homework Statement
Find the distance between (2,5,1) and the line 2i − 3j + 6k.
Distance between a point and a line in space
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Homework Help Overview
The discussion revolves around finding the distance between a point in space, specifically (2,5,1), and a line represented by the vector 2i − 3j + 6k. Participants are exploring the nature of the vector and its relation to the concept of a line in three-dimensional space.
Discussion Character
- Conceptual clarification, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Some participants question whether the given vector represents a line or just a direction. There are attempts to clarify the problem statement and the correct interpretation of the vector in relation to the point.
Discussion Status
The discussion is ongoing, with participants providing insights into the nature of the vector and its implications for the problem. Some guidance has been offered regarding the use of distance formulas and vector math, although there is no consensus on the correct approach yet.
Contextual Notes
Participants mention the need to adhere to forum rules regarding providing attempts before receiving help, and there are indications of confusion regarding notation and terminology related to vectors and lines.
Find the distance between (2,5,1) and the line 2i − 3j + 6k.
- #2
Gunthi
- 65
- 1
lockedup said:
It's a plane.
- #3
Mark44
Mentor
- 38,107
- 10,661
No, it isn't.Gunthi said:
- #4
Mark44
Mentor
- 38,107
- 10,661
2i - 3j + 6k isn't a line -- it's a vector. It has a certain length, while a line has infinite length. The problem is probably something more like this:lockedup said:
Find the distance between (2,5,1) and the line whose direction is given by the vector 2i − 3j + 6k.
Just as well. Given that you can't find a formula, how would you approach this problem? According to the forum rules, you have to give it a good shot before anyone can give you any help.lockedup said:
- #5
pootette
- 9
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Gunthi,
I believe you are asking how to find the distance between a point in space, and a vector?
If so, start by looking at line-distance formulas and vector math.
I hope this gives you a jumping-off point.
I believe you are asking how to find the distance between a point in space, and a vector?
If so, start by looking at line-distance formulas and vector math.
I hope this gives you a jumping-off point.
- #6
lockedup
- 67
- 0
My assignment sheet says line...Mark44 said:
Does 20 or so google searches count? I've clicked on numerous links, some from here, and none of it makes any sense.
The formula in my Calculus book states:
D = \frac{||PQ \times u||}{||u||}
P is a point on the line, Q is the point in space, and u is the direction vector. Since I'm only given a vector and as opposed to a line, can I use (0, 0, 0) for P so that PQ is just Q?
- #7
Mark44
Mentor
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Sure, give your formula a shot.
And no, Google searches don't count...
And no, Google searches don't count...
- #8
Gunthi
- 65
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Mark44 said:
You're right, I confused notation, sorry lockedup.
- #9
Gunthi
- 65
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pootette said:
That was not my question.
- #10
Mark44
Mentor
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Gunthi,
If it were 2x - 3y + 6z = 0, you would be right
If it were 2x - 3y + 6z = 0, you would be right
- #11
Gunthi
- 65
- 1
Mark44 said:
Yes, that was what I thought initialy.
I'm just not accostumed to working with i,j,k.
- #12
pootette
- 9
- 0
The formula wants you to multiply the scalar (point) by a unit vector and cross multiply with the given vector. Take the magnitude of the resultant vector. Then divide by magnitude of the unit vector (just a step that has to be done - balances things out 
. This will give a scalar quantity of distance.
. This will give a scalar quantity of distance.
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