1.

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

Answer» Correct Answer - B
Let the direction ratios of the normal to the plane be proportional to a,b,c. Then, the equation of the plane is
`a(x-1)+b(y-0)+c(z-0)=0`……………i
It passes through (0,1,0)
`:.a(-1)+b(1)+c(0)=0impliesa=b`…………….ii
It is given that the plane i makes an angle `pi//4` with the plane `x+y=3`.
`:."cos"(pi)/4=(axx1+bxx1+cxx0)/(sqrt(a^(2)+b^(2)+c^(2))sqrt(1+1))`
`implies1/(sqrt(2))=(a+b)/(sqrt(a^(2)+b^(2)+c^(2))sqrt(2))`
`impliessqrt(a^(2)+b^(2)+c^(2))=a+b`
`impliesa^(2)+b^(2)+c^(2)=a^(2)+b^(2)+2abimpliesc^(2)=2ab`............iii
From ii and iii, we have
`a:b:c=a:a:sqrt(2)a=1:1:sqrt(2)`


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