A bird is moving with velocity ` 10 ms?^(-1)` in a direction making an angle of ` 60^@` with vertical upward. Represent the velocity vector in rectangular form.

Explanation

Let eastern line be along Z-axis, borthrn line along Y-axis and vertical uupward line along Z-axis, Let the velcity of bird ` vec v` make angles ` alpha, beta, gamma = 60^@`.
As ` cos^2 alpha + cos^2 gamma =1`
ro 1 ( cos 60^@)^2 + cos^2 beta + (cos 60^2)^2= 1` ltbRgt or ` 1/4 + cos^2 beta + 1/4 = 1 ` or cos^2 beta 1 - 1/2 1/2 = 1/2`
` cos beta = `1/( sqrt 2) = cos 45^@ ` or beta = 45^2`
:. vec v = v cos alpha hat i + v cos beta hat j _ v cos gaama hat ltbRrgt` 10 xxx 1 ( sqrt2 ) hat j + 10cos 60^2 hat k`
` = ( 5 hat i+ 5 sqrt hat j + 5 hat k)`.