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If the projections of vector vec a o...

If the projections of vector ` vec a` on `x` -, `y` - and `z` -axes are 2, 1 and 2 units ,respectively, find the angle at which vector ` vec a` is inclined to the `z` -axis.

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Since projections of vector `veca` on x-, y- and z-axes are 2, 1 and 2 units, respectively, we have
`" ""Vector "veca=2hati+hatj+2hatk`
`" "|veca|=sqrt(2^(2)+1^(2)+2^(2))=3`
Then `cosgamma=(2)/(3)` (where `gamma` is the angle of vector `veca` with the z-axis), i.e.,
`" "gamma=cos^(-1)""(2)/(3)`
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