JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q15

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MathematicsSingle correct+4 / -1Question 15 of 90

If two distinct points Q, R lie on the line of intersection of the planes $-x+2y-z=0$ and $3x-5y+2z=0$ and $PQ=PR=\sqrt{18}$ where the point P is $(1,-2,3)$ , then the area of the triangle PQR is equal to

\dfrac23\sqrt{38}

\dfrac43\sqrt{38}

\dfrac83\sqrt{38}

\sqrt{\dfrac{152}3}

Answer and worked solution

Official answer: B

Line. Direction $(-1,2,-1)\times(3,-5,2)=(-1,-1,-1)$ , through the origin.

Distance of P. $\dfrac{|(1,-2,3)\times(1,1,1)|}{\sqrt3}=\dfrac{|(-5,2,3)|}{\sqrt3}=\sqrt{\frac{38}3}$ .

Half of QR. $\sqrt{18-\frac{38}3}=\frac4{\sqrt3}$ .

Area $=\frac4{\sqrt3}\cdot\sqrt{\frac{38}3}=\frac43\sqrt{38}$ .

(B)

Topics:Angles and distances Equation of a line in space

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JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 15