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.

Explanation

Let us take eastern lines as x-asis, vertical upwards line as ` Z-axis and the line perpende-cular to both ,say northward line as y-axis . Let
` alpha` beta` and ` gamma` be the angles which ` vec v` make, with x-axis , y-axis and z-axis respectively. ltbRgt Here, ` cos alpha = cos 60^@ = 1//2 ,`
`cos gamma = cos 60^2 = 1//2 `
As,` cos ^@ alpha + cos^2 beta+ cos ^2 gamma =1`
So ` ( 1/2)^2 = c0s^2 beta + (1/2) ^2 = 1`
or ` cos^2 beta = 1 /(sqrt 2) `
As velocity, ` vec v_x hat i + v_y hat j + v_z kat k`
`= (v cos alpha) hat i + (v cos beta0 hat j + ( v cos gamma) hat k`
:.
`vec v = ( 20 xx 1/2 ) hat i + ( 20 xx 1/(sqrt 2)0 hat j +(20 xx 1/2 0hat k`
` =10 haat i + 10 sqrt 2 hat j + 10 hat k`.