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Question
Find the direction cosines and direction ratios for the following vector
`3hat"i" - 3hat"k" + 4hat"j"`
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Solution
The direction ratio of the vector `3hat"i" - 3hat"k" + 4hat"j"` are (3, 4, – 3)
The direction cosines of the vector `3hat"i" - 3hat"k" + 4hat"j"` are
`3/sqrt(3^2 + 4^2 + (-3)^2), 4/sqrt(3^2 + 4^2 + (-3)^2), (-3)/sqrt(3^2 +4^2 + (-3)^2)`
`3/sqrt(9 + 16 + 9), 4/sqrt(9 + 16 + 9), (-3)/sqrt(9 + 16 + 9)`
`(3/sqrt(34), 4/sqrt(34), (-3)/sqrt(34))`
Direction ratios = (3, 4, – 3)
Directio cosines = `(3/sqrt(34), 4/sqrt(34), (-3)/sqrt(34))`
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