A bird moves with velocity 20m/s in a direction making an angle of `60^(@)` with the eastern line and `60^(@)` with the vertical upward. Represent the velocity vector in rectangular form.
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Let eastern line by taken as x-axis, northern as y-axis and vertical upward as z-axis
Let the velocity `vecv` makes angle `alpha,beta` and `gamma` with x,y and z axis respectively, then `alpha=60^(@)`, `gamma=60^(@)` we have
`cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
`cos^(2)60^(@)+cos^(2)beta+cos^(2)60^(@)=1`
`cos^(2)beta=(1)/(2), cos beta=(1)/sqrt(2)`
so `vecv=v cos alpha hati+v cos beta hatj+v cos gammahatk`
`=20[(1)/(2)hati+(1)/sqrt(2)hati+(1)/(2)hatk]`
`=10hati+10sqrt(2)hatj+10hatk`