The x-y plane is rotated about its line of intersection with the y-z plane by `45^0` , then the equation of the new plane is/are a. `z+x=0` b. `z-y=0` c. `x+y+z=0` d. `z-x=0`

Options

A. `z+x=0`
B. `z-y=0`
C. `x+y+z=0`
D. `z-x=0`

Answer

a, d

Explanation

The equation of a plane passing through the line of intersection of the `x-y and y-z` planes is
`" "z+lamdax=0, lamdain R`
This plane makes an angle `45^(@)` with the `x-y` plane `(z=0)`. Thus,
`" "cos45^(@) = (1)/(sqrt(1)sqrt(lamda^(2)+1))`
or `" "lamda= pm 1`