A bird moves with velocity ` 10 ms^(-1)` in a direction making an angle if ` 60 ^@` with the eastern derction and ` 45^@` with vertical upward direction. Represent the velocity vector of bird in rectanular form.

Explanation

Let the eastern line be taken as X-axis, the northern line be taken as Y-axis and vertical upward direction as Z-axis. Let the velcoity vector` vec v` of the movig bird makes angles ` alpha` , beta` and gamma` with ` X-Y` and Z-axes respectively. Then
` alpha = 60^@, gamma = 45^@`,
As ` cos^2 alpha + cos^@ beta + cas^2 gamma=1`
:. ` cos^2 60^@ beta + ( 1/( sqrt 2))^2 = 1` ltbRgt or ` cos^@ beta = 1 - 1/4 - 1/2 = 1/4 ` or `cos beta = 1/2`
:. ` vec v = v cos alpha hat i+ 10 xx 1/2 hat j + 10 xx 1/( sqrt2 ) hat k` ltbr ` = 5 hat i+ 5 aht j+ 5 sqrt 2 hat k`.