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Question
If a unit vector `veca` makes angles `pi/3` with `hati,pi/4` with `hatj` and acute angles θ with ` hatk,` then find the value of θ.
Solution
Let `veca=xhati+yhatj+zhatk` be the unit vector
`therefore x=cospi/3=1/2`
`y=cospi/4=1/sqrt2`
Now
` x^2+y^2+z^2=1`
`(1/2)^2+(1/sqrt2)^2+z^2=1`
`z^2=1-1/4-1/2=1/4`
`z=1/2`
`costheta=1/2`
`theta=pi/3`
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