A straight line `L` on the xy-plane bisects the angle between `O Xa n dO Ydot` What are the direction cosines of `L ?` a. `((1//sqrt(2)),(1//sqrt(2)),0)` b. `((1//2),(sqrt(3)//2),0)` c. `(0,0,1)` d. (2/3, 2/3, 2/3)

Options

A. `lt(1//sqrt2),(1//sqrt2),0gt`
B. `lt(1//2),(sqrt3//2),0gt`
C. `lt0,0,1gt`
D. `lt(2//3),(2//3),(1//3)gt`

Answer

a

Explanation

The given line makes angles of `pi//4, pi//4 and pi//2` with the `x-, y- and z-`axes, respectively.
Hence, direction cosines of the given line are
`" "cos(pi//4), cos(pi//4) and cos(pi//2)`, or
`" "(1//sqrt2), (1//sqrt2)` and 0.