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A surveyor writes down four sets of three numbers as… | StemPy Lab
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A surveyor writes down four sets of three numbers as possible direction cosines of a line in the plan of a hall. Only one of the sets can be the direction cosines of a real line. Which one is it?
Mathematics
Easy
High School (11–12)
Vectors and Three-Dimensional Geometry › Three-Dimensional Geometry
A-Level
IB
Created by
StemPy Lab
A surveyor writes down four sets of three numbers as possible direction cosines of a line in the plan of a hall. Only one of the sets can be the direction cosines of a real line. Which one is it?
1
2
,
1
2
,
1
2
\dfrac{1}{2},\ \dfrac{1}{2},\ \dfrac{1}{\sqrt{2}}
2
1
,
2
1
,
2
1
1
3
,
1
3
,
1
3
\dfrac{1}{3},\ \dfrac{1}{3},\ \dfrac{1}{3}
3
1
,
3
1
,
3
1
2
3
,
2
3
,
2
3
\dfrac{2}{3},\ \dfrac{2}{3},\ \dfrac{2}{3}
3
2
,
3
2
,
3
2
1
2
,
1
2
,
1
2
\dfrac{1}{2},\ \dfrac{1}{2},\ \dfrac{1}{2}
2
1
,
2
1
,
2
1
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← The three vectors i + 2 k, j + k and 2 i + 3 j + λ k lie in one plane for one value of λ. What is it?
A pipe runs from the point P(3, -2, 4) to the point Q(4, 2, 12), with coordinates in metres. Which set gives the direction cosines of the line PQ in the direction from P to Q? →
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