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Question
Find the direction cosines of a vector whose direction ratios are
1, 2, 3
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Solution
The given direction ratios are a = 1, b = 2, c = 3
If a, b, c are the direction ratios of a vector then the direction cosines of the vector are
l = `"b"/sqrt("a"^2 +"b"^2 + "c"^2)`
m = `"b"/sqrt("a"^2 + "b"^2 + "c"^2)`
c = `"c"/sqrt("a"^2 + "b"^2 +""^2)`
∴ The required direction cosines of thee vector are
`1/sqrt(1^2 + 2^2 + 3^2), 2/sqrt(1^2 + 2^2 + 3^2), 3/sqrt(1^2 + 2^2 + 3^2)`
`1/sqrt(1 + 4 + 9), 2/sqrt(1 + 4 + 9), 3/sqrt(1 + 4 + 9)`
`(1/sqrt(14), 2/sqrt(14), 3/sqrt(14))`
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