The dr. of normal to the plane through `(1,0,0), (0,1,0)` which makes an angle `pi/4` with plane , `x+y=3` are

Options

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

Answer

B

Explanation

Let the equation of place in intercept form is `(x)/(a)+(y)/(b)+(z)/(c )=1`
Since, it passes through the points (1, 0, 0) and (0, 1, 0).
`therefore` Equation of plane is
`(x)/(1)+(y)/(1)+(z)/(c )=1`
DR's or normal of plane
`(x)/(1)+(y)/(1)+(z)/(c ) =1" are " 1, 1, (1)/(c ) ` and of given plane are 1, 1, 0.
Now, ` "cos"(pi)/(4)=(1*1+1*1+(1)/(c )*0)/((sqrt((1)/(c^(2))+2))sqrt(2))`
`rArr (1)/(c^(2))+2=4`
`rArr c^(2)=(1)/(2)`
`rArr c=(1)/(sqrt(2))`
`therefore` DR's of normal are `1,1, sqrt(2).`