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Show that the vector veci+vecj+veck is ...

Show that the vector `veci+vecj+veck` is equally inclined to the axes OX, OY and OZ.

Text Solution

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Let `a=hati+hatj+hatk`
If a makes angles `alpha,beta,gamma` with X,Y and Z-axes respectively, then
`cosalpha=(1)/(sqrt(1^(2)+1^(2)+1^(2)))=(1)/(sqrt(3))`
`cos beta=(1)/(sqrt(3))`
and `cos gamma=(1)/(sqrt(3))`
Thus, we have `cos alpha=cosbeta=cosgamma,` i.e., `alpha=beta=gamma`
Hence, a is equally inclined to the axes.
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