Find the angles at which the following vectors are inclined to each of the coordinate axes: ` hat i- hat j+ hat k`

Explanation

The given vector is ` hat{i}- hat{j}+hat{k}`

Unit vector `=frac{ hat{i}-hat{j}+hat{k}}{| hat{i}- hat{j}+hat{k}|}`
`=frac{1}{sqrt{3}} hat{i}+frac{-1}{sqrt{3}} hat{j}+frac{1}{sqrt{3}} hat{k}`
So, `quad cos alpha=frac{1}{sqrt{3}} `
`Rightarrow alpha=cos ^{-1}(frac{1}{sqrt{3}} ) `


`cos beta= frac{-1}{sqrt{3}} Rightarrow beta=cos ^{-1}( frac{-1}{sqrt{3}})`



`cos gamma=frac{1}{sqrt{3}`
`Rightarrow gamma=cos ^{-1}(frac{1}{sqrt{3}})`


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