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Question
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are ______.
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Solution
The direction cosines of vector `(2hat"i" + 2hat"j" - hat"k")` are `2/3, 2/3, (-1)/3`.
Explanation:
Let `vec"a" = 2hat"i" + 2hat"j" - hat"k"`
Direction ratios of `vec"a"` are 2, 2, – 1
So, the direction cosines are `2/sqrt(4 + 4 + 1)`
`2/sqrt(4 + 4 + 1)`
`-1/sqrt(4 + 4 + 1)`
⇒ `2/3, 2/3, (-1)/3`
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