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प्रश्न
A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.
पर्याय
`+-(1, 1, 1)`
`+-(1/sqrt(3), 1/sqrt(3), 1/sqrt(3))`
`+-(1/3, 1/3, 1/3)`
`+-(1/sqrt(3), (-1)/sqrt(3), (-1)/sqrt(3))`
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उत्तर
A line makes equal angles with co-ordinate axis. Direction cosines of this line are `+-(1/sqrt(3), 1/sqrt(3), 1/sqrt(3))`.
Explanation:
Let the line makes angle α with each of the axis.
Then, its direction cosines are cos α, cos α, cos α.
Since cos2α + cos2α + cos2α = 1.
Therefore, cos α = `+- 1/sqrt(3)`.
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