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Question
Find the direction cosines of a vector whose direction ratios are
`1/sqrt(2), 1/2, 1/2`
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Solution
The given direction ratios are a = 3, b = – 1 , c = 3
If a, b, c are the direction ratios of a vector ten the direction cosines of the vector are
l = `"b"/sqrt("a"^2 + "b"^2 + "c"^2)`
m = `"b"/sqrt("a"^2 + "b"^2 + "c")`
c = `"c"/sqrt("a"^2 + "b"^2 + "c")`
∴ The required direction cosioes of the water are
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`(-1)/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(3^2 + (-1)^2 + 3^2)`
`3/sqrt(9 + 1 + 9)`
`(- 1)/sqrt(9 + 1 + 9)`
`3/sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1)/sqrt(9 + 1+ 9))`
`3/sqrt(9 + 1 + 9)`
`1/sqrt(19), (-1)/sqrt(19)`
= `3sqrt(9 + 1 + 9)`
`(3/sqrt(19), (-1) /sqrt(19), 3/sqrt(19))`
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