- #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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SUMMARY
The discussion focuses on calculating the distance between the point (2,5,1) and the line defined by the direction vector 2i − 3j + 6k. Participants clarify that the vector itself is not a line but can be used to derive the distance using vector math. The formula provided for this calculation is D = ||PQ × u|| / ||u||, where P is a point on the line, Q is the point in space, and u is the direction vector. The conversation emphasizes the importance of understanding vector notation and the correct application of distance formulas in three-dimensional space.
PREREQUISITES- Understanding of vector notation (i, j, k)
- Familiarity with vector cross product
- Knowledge of distance formulas in three-dimensional geometry
- Basic calculus concepts related to vectors
- Study vector cross product calculations in depth
- Learn about distance formulas between points and lines in 3D space
- Explore vector projections and their applications
- Review examples of solving distance problems involving vectors
Students in mathematics or physics, educators teaching vector calculus, and anyone seeking to understand spatial relationships in three-dimensional geometry.
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
- 38,083
- 10,618
No, it isn't.Gunthi said:
- #4
Mark44
Mentor
- 38,083
- 10,618
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
- 38,083
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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
- 38,083
- 10,618
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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