A bird moves with velocity `20m s^(-1)` in a direction making an angle of `60^(@)` with vertical upward .Represent the velocity vector in a rectangular form.

A bird moves with velocity `20m s^(-1)` in a direction making an angle

1.	A bird moves with velocity `20m s^(-1)` in a direction making an angle of `60^(@)` with vertical upward .Represent the velocity vector in a rectangular form.
Answer» Let the easten line be taken as x-axis ,northen as y-axis,and vertical upward as z-axis . Let the velocity`v` makes angles `alpha, beta`, and `gamma` with x-, y- and z-axis, respectively. Then `alpha=60^(@)` and `gamma=60^(@)`. `cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1` We have `cos^(2)60^(@)+cos^(2)beta+cos^(2)60^(@)=1` or `cos beta=1/sqrt(2)` ` vec(v)=vcos alpha hat(i)+v cos beta hat (j)+v cos gamma hat(k)` `=20[1/2hat(i)+1/sqrt(2)hat(j)+1/2hat(k)]=10hat(i)+10sqrt(2)hat(j)+10hat(k)`

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A bird moves with velocity `20m s^(-1)` in a direction making an angle of `60^(@)` with vertical upward .Represent the velocity vector in a rectangular form.

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