JEE Advanced 2017 · Paper 2 · Mathematics Q1

MathematicsSingle correct+3 / -1Question 37 of 54

The equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to the planes $2x + y - 2z = 5$ and $3x - 6y - 2z = 7$ , is

14x + 2y - 15z = 1

14x - 2y + 15z = 27

14x + 2y + 15z = 31

-14x + 2y + 15z = 3

Answer and worked solution

Official answer: C

Normal. The plane's normal is perpendicular to both given normals:
$(2,1,-2)\times(3,-6,-2)=(-14,-2,-15)\ \parallel\ (14,2,15).$

Through (1, 1, 1). $14x+2y+15z=14+2+15=31$ .

(C)

Topics:Equation of a plane Cross product

JEE Advanced 2017 · Paper 2, Mathematics question 1