JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q84

MathematicsSingle correct+4 / -1Question 84 of 90

The equation of the plane containing the line $2x-5y+z=3$ ; $x+y+4z=5$ , and parallel to the plane, $x+3y+6z=1$ , is :

2x+6y+12z=13

x+3y+6z=-7

x+3y+6z=7

2x+6y+12z=-13

Answer and worked solution

Official answer: C

Take $(2x-5y+z-3)+\lambda(x+y+4z-5)=0$ with normal parallel to (1, 3, 6). From $\frac{2+\lambda}1=\frac{\lambda-5}3$ , $\lambda=-\frac{11}2$ .

The plane is $-3.5x-10.5y-21z+24.5=0$ , i.e. $x+3y+6z=7$ .

JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 84