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.

A bird moves with velocity 20m/s in a direction making an angle of `60

1.	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.
Answer» 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`

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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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