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Question
Find the direction cosines and direction ratios for the following vector
`5hat"i" - 3hat"j" - 48hat"k"`
Solution
The direction ratios of the vector `5hat"i" - 3hat"j" - 48hat"k"` are (5, – 3, – 48)
The direction cosines of the vector `5hat"i" - 3hat"j" - 48hat"k"` are
`5/sqrt(5^2 + (-3)^2 + (-48)^2), (-3)/sqrt(5^2 + (-3)^2 + (-48)^2), (-48)/sqrt(5^2 + (-3)^2 + (-48)^2)`
`5/sqrt(25 + 9 + 2304), (-3)/sqrt(25 + 9 + 2304), (-48)/sqrt(25 + 9 + 2304)`
`(5/sqrt(2338), (-3)/sqrt(2338), (-4)/sqrt(2338))`
Direction ratios = (5, – 3, – 48)
Direction cosies = `(5/sqrt(2338), (-3)/sqrt(2338), (-4)/sqrt(2338))`
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