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Question
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 4hat"j" + 8hat"k"`
Solution
The direction ratios of the `3hat"i" - 4hat"j" + 8hat"k"` are (3, – 4, 8)
The direction cosines of the vector `3hat"i" - 4hat"j" + 8hat"k"` are
`3/sqrt(3^2 + (-4)^2 + 8^2),(-4)/sqrt(3^2 + (-4)^2 + 8^2), 8/sqrt(3^2 + (-4)^2 + 8^2)`
`3/sqrt(9 + 16 + 64), (-4)/sqrt(9 + 16 + 64), 8/sqrt(9 + 16 + 64)`
`(3/sqrt(89), (-4)/sqrt(89), 8/sqrt(89))`
Direction ratios = (3, – 4, 8)
Direction cosines = `(3/sqrt(89), (-4)/sqrt(89), 8/sqrt(89))`
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