Find the angles at which the following vectors are inclined to each of the coordinate axes: `4 hat i+8 hat j+ hat k`

Explanation

The given vector is `4 hat{i}+8 hat{j}+hat{k}`

Unit vector `=frac{6 hat{i}+8 hat{j}+hat{k}}{|4 hat{i}+8 hat{j}+hat{k}|}`
`=frac{4}{9} hat{i}+frac{8}{9} hat{j}+frac{1}{9} hat{k}`
So, `quad cos alpha=frac{4}{9}`
`Rightarrow alpha=cos ^{-1}(frac{4}{9})`


`cos beta=frac{8}{9} Rightarrow beta=cos ^{-1}(frac{8}{9})`



`cos gamma=frac{1}{9} Rightarrow gamma=cos ^{-1}(frac{1}{9})`


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