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प्रश्न
A vector `vec"r"` is inclined at equal angles to the three axes. If the magnitude of `vec"r"` is `2sqrt(3)` units, find `vec"r"`.
उत्तर
Since, the vector `vec"r"` makes equal angles with the axes, their direction cosines should be same
∴ l = m = n
We know that l2 + m2 + n2 = 1
⇒ l2 + l2 + l2 = 1
⇒ 3l2 = 1
⇒ l2 = `1/3`
⇒ l = `+- 1/sqrt(3)`
∴ `hat"r" = +- 1/sqrt(3)hat"i" +- 1/sqrt(3)hat"j" +- 1/sqrt(3)hat"k"`
⇒ `hat"k" = +- 1/sqrt(3) (hat"i" + hat"j" + hat"k")`
We know that `vec"r" = (hat"r") |vec"r"|`
= `+- 1/sqrt(3) (hat"i" + hat"j" + hat"k") 2sqrt(3)`
= `+- 2(hat"i" + hat"j" + hat"k")`
Hence, the required value of `vec"r"` is `+- 2(hat"i" + hat"j" + hat"k")`.
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