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Question
Find the direction cosines and direction ratios for the following vector
`3hat"i" + hat"j" + hat"k"`
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Solution
The direction ratios of the vector `3hat"i" + hat"j" + hat"k"` are (3, 1, 1)
The direction cosines of the vector `3hat"i" + hat"j" + hat"k"` are
`3/sqrt(3^2 + 1^2 + 1^2), 1/sqrt(3^2 + 1^2 + 1^2), 1/sqrt(3^2 + 1^2 + 1^2)`
`3/sqrt(9 + 1 + ), 1/sqrt(9 + 1 + 1), 1/sqrt(9 + 1 + 1)`
`(3/sqrt(11), 1/sqrt(11), 1/sqrt11)`
Direction ratios = (3, 1, 1)
Direction cosines = `(3/sqrt(11), 1/sqrt(11), 1/sqrt11)`
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