Write a vector of magnitude 12 units which makes `45^0` angle with X-axis `60^0` angle with Y-axis and an obtuse angle with Z-axis.

Explanation

Given, `l=cos45^@` and `m=cos 60^@`

`implies l=1/sqrt2, m=1/2`

As, `l^2+m^2+n^2=1`

`implies 1/2+1/4+n^2=1`

`implies n=pm1/2`

`implies n=-1/2` (as angle is obtuse)

Thus, required vector is `12(lhati+mhatj+nhatk)`

`=12(1/sqrt2hati+1/2hatj-1/2hatk)`

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