Student 999
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Confused as to why my method doesn't work, when find ing the normal vector it gives 0 why is this the case when all three points lie on the same planeName:  Screenshot 2022-05-18 at 16.34.29.png
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ghostwalker
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(Original post by Student 999)
Confused as to why my method doesn't work, when find ing the normal vector it gives 0 why is this the case when all three points lie on the same plane
Not sure what "method" you're using, but as to your question: Think about it. Under what circumstances is the cross product of two vectors zero?
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Student 999
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(Original post by ghostwalker)
Not sure what "method" you're using, but as to your question: Think about it. Under what circumstances is the cross product of two vectors zero?
My method is to find two direction vectors that lie on the plane then find the equation of plane by finding the normal vector and sub the three points in to prove they lie on the plane. When crossing the vectors its 0 when they're perpendicular to each other. However since a b and c lie on the plane unless ab and ac have an angle of 90 between each other shouldn't it work in finding the normal vector to both directions?
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mqb2766
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(Original post by Student 999)
My method is to find two direction vectors that lie on the plane then find the equation of plane by finding the normal vector and sub the three points in to prove they lie on the plane. When crossing the vectors its 0 when they're perpendicular to each other. However since a b and c lie on the plane unless ab and ac have an angle of 90 between each other shouldn't it work in finding the normal vector to both directions?
It wants you to show vectors OA, OB, OC lie in the same plane, so no need to difference them.
However, the bold sounds like youre thinking of the dot (scalar) product, not the cross (vector) product. When does the cross product break down (equal 0)? Just looking at your AB and AC you should be able to guess?
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Student 999
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(Original post by mqb2766)
It wants you to show vectors OA, OB, OC lie in the same plane, so no need to difference them.
However, the bold sounds like youre thinking of the dot (scalar) product, not the cross (vector) product. When does the cross product break down (equal 0)? Just looking at your AB and AC you should be able to guess?
Still can't seem to understand it, AB isn't perpendicular to AC in my sketch? Could you break down the explanation a bit more thanks
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mqb2766
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(Original post by Student 999)
Still can't seem to understand it, AB isn't perpendicular to AC in my sketch? Could you break down the explanation a bit more thanks
AB and AC are certainly not perpendicular, they're ...
What is the cross (vector) product formula and what is the dot (scalar) product formula, as per the previous post?

But note the question is asking about vectors a, b and c (not points), so its not correct to difference them in answering the question.
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Student 999
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(Original post by mqb2766)
AB and AC are certainly not perpendicular, they're ...
What is the cross (vector) product formula and what is the dot (scalar) product formula, as per the previous post?

But note the question is asking about vectors a, b and c (not points), so its not correct to difference them in answering the question.
My bad, I kept thinking of cos, its when the angle between two vectors is 0. Also that makes as they're vectors not points. I would just find the cross product between two vectors and dot it with the final vector, if equals 0 then they're parallel and lie on the same plane
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mqb2766
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(Original post by Student 999)
My bad, I kept thinking of cos, its when the angle between two vectors is 0. Also that makes as they're vectors not points. I would just find the cross product between two vectors and dot it with the final vector, if equals 0 then they're parallel and lie on the same plane
Agreed about cos() for dot and sin() for cross. So do was you say, its fairly obvious that the third vector is a simple linear combination of the other two which is what the question is askign about. However, note that the bold still isn't correct. If the dot is 0, you can conclude the vectors lie in the same plane. Thats it. You can't conclude theyre (which ones?) are parallel.

The end points of the 3 vectors in this question all lie on a line, hence the difference between any two of the vectors has the same direction vector (down to a scalar multiple). This isn't necessary for 3 vectors lying on a plane as should be obvious. You could multiply c by 2, and the 3 vectors would lie on a plane, but the difference vectors wouldn't be parallel.
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