Write the direction cosines of the vector `-2 hat i+ hat j-5 hat k`

Explanation

Here, direction ratios of the given vector are `(-2,1,-5)`.

Let direction cosines of the given vector are `(-2k,k,-5k)`, where `k` is a positive number.

Then, `(-2k)^2+(k)^2+(5k)^2 = 1`

`=>4k^2+k^2+25k^2 = 1`

`=>30k^2 = 1`

`=>k^2 = 1/30`

`=> k =1/sqrt30`

`:.` Direction cosines of the given vector are `(-2/sqrt30,1/sqrt30,-5/sqrt30)`.