A vector ` vec r` is inclined at equal acute angles of `x-a xi s ,` `y-a xi s` and `z-a xi sdot` if `| vec r|=6` units, find ` vec rdot`

Explanation

As the given line is equally inclined with all three coordinate axis,
let it create angle `alpha` with all three coordinate axis.

Then,

Direction cosines will be `(cos alpha,cos alpha,cos alpha)`.

`:. cos^2alpha+cos^2alpha+cos^2alpha = 1`

`=>3cos^2alpha = 1`

`=>cos alpha = +-1/sqrt3`

Since `vecr` is inclined at acute angle, therefore, `cos alpha = 1/sqrt3`.

Direction cosines will be `(1/sqrt3,1/sqrt3,1/sqrt3)`.

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