If a line makes angles `90o," "135o," "45o` with the x, y and z-axes respectively, find its direction cosines.

Options

A. `0,(1)/(sqrt(2)), - (1)/(sqrt(2))`
B. `0, - (1)/(sqrt(2)), - (1)/(sqrt(2))`
C. `1, (1)/(sqrt(2)), (1)/(sqrt(2))`
D. `0, - (1)/(sqrt(2)), (1)/(sqrt(2))`

Explanation

The line makes angle `90^(@), 135^(@), 45^(@)` with X,Y and Z - axes respectively.
Here `alpha = 90^(@) , beta = 135^(@) , gamma = 45^(@)`
So , direction consines are
`cos alpha = cos 90^(@) = 0`
`cos beta = cos 135^(@) = - (1)/(sqrt(2))`
`cos gamma = cos 45^(@) = (1)/(sqrt(2))`
So, direction cosines are `(0, - (1)/(sqrt(2)),(1)/(sqrt(2)))`
Hence , the correct answer form the given alternatives is (d).