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Question
Find the direction cosines and direction ratios for the following vector
`hat"i" - hat"k"`
Solution
The direction ratios of the vector `hat"i" + 0hat"j" - hat"k"` are (1, 0, – 1)
The direction cosines of the vector `hat"i" + 0hat"j" - hat"k"` are
`1/sqrt(1^2 + 0^2 + (-1)^2), 0/sqrt(1^2 + 0^2 + (-1)^2), (-1)/sqrt(1^2 + 0^2 + (-1)^2)`
`1/sqrt(1 + 0 + 1), 0/sqrt(1 + 0 + 1), (-1)/sqrt(1 + 0 + 1)`
`(1/sqrt(2), 0, (-1)/sqrt(2))`
DIrection ratios = (1, 0, – 1)
Direction cosines = `(1/sqrt(2), 0, (-1)/sqrt(2))`
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