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Question
Show that the vector `hati + hatj + hatk` is equally inclined to the axes OX, OY, and OZ.
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Solution
Let `veca = hati + hatj + hatk`
Then,
`|veca| =sqrt(1^2 + 1^2 + 1^2) = sqrt3`
Therefore, the direction cosines of `veca` are `(1/sqrt3, 1/sqrt3, 1/sqrt3)`.
Now, let α, β, and λ be the angles formed by `veca` with the positive directions of the x, y, and z axes.
Then, we have `cosalpha = 1/sqrt3, cosbeta = 1/sqrt3, coslambda = 1/sqrt3`.
Hence, the given vector is equally inclined to axes OX, OY, and OZ.
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