JEE Main201911 Jan 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The direction ratios of normal to the plane through the points (0,-1,0) and (0,0,1) and making an angle 4 with the plane y-z+5=0 are; 2,-1,1 2, 2 - 2 2 , 1,-12 3 , 1,-1

Options

Aoption 1 and 2
Boption 2 and 3
Coption 3 and 4
Dall the options

Correct answer

B. option 2 and 3

Step-by-step solution

Let the d.r's of the normal be a, b, c Equation of the plane is a(x-0)+b(y+1)+c(z-0)=0 It passes through (0,0,1) b+c=0 Also 0 a+b-c a²+b²+c² 2 = 4 = 1 2 b-c= a²+b²+c² And b+c=0 b= 1 2 a The d.r's are 2 , 1,-1 or 2, 2 ,- 2

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