JEE Main 2022 · 25 Jun · Shift 2 · Mathematics Q9

← JEE Main 2022 · 25 Jun · Shift 2

MathematicsSingle correct+4 / -1Question 9 of 90

Let $P$ be the plane passing through the intersection of the planes $\vec r\cdot\left(\hat i+3\hat j-\hat k\right)=5$ and $\vec r\cdot\left(2\hat i-\hat j+\hat k\right)=3$ , and the point $(2,1,-2)$ . Let the position vectors of the points $X$ and $Y$ be $\hat i-2\hat j+4\hat k$ and $5\hat i-\hat j+2\hat k$ respectively. Then the points

X

and

X+Y

are on the same side of

P

Y

and

Y-X

are on the opposite sides of

P

X

and

Y

are on the opposite sides of

P

X+Y

and

X-Y

are on the same side of

P

Answer and worked solution

Official answer: C

Plane P. $(x+3y-z-5)+\lambda(2x-y+z-3)=0$ through $(2,1,-2)$ : $2-2\lambda=0$ , $\lambda=1$ , so P is $3x+2y-8=0$ .

Signs. X $(1,-2,4)$ : $3-4-8=-9$ . Y $(5,-1,2)$ : $15-2-8=5$ . Opposite signs: X and Y are on opposite sides.

(C)

Topics:Equation of a plane

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JEE Main 2022 · 25 Jun · Shift 2, Mathematics question 9