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A student writes down four sets of three numbers and… | StemPy Lab
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A student writes down four sets of three numbers and claims that one of them can be the direction cosines of a line in space. Which set is possible?
Mathematics
Medium
High School (11–12)
Vectors and Three-Dimensional Geometry › Vector Algebra
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A student writes down four sets of three numbers and claims that one of them can be the direction cosines of a line in space. Which set is possible?
2
3
,
2
3
,
2
3
\dfrac{2}{3},\ \dfrac{2}{3},\ \dfrac{2}{3}
3
2
,
3
2
,
3
2
1
3
,
1
3
,
1
3
\dfrac{1}{3},\ \dfrac{1}{3},\ \dfrac{1}{3}
3
1
,
3
1
,
3
1
2
3
,
−
1
3
,
2
3
\dfrac{2}{3},\ -\dfrac{1}{3},\ \dfrac{2}{3}
3
2
,
−
3
1
,
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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