JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q30

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MathematicsInteger+4 / -1Question 30 of 90

Let Q and R be two points on the line $\dfrac{x+1}2=\dfrac{y+2}3=\dfrac{z-1}2$ at a distance $\sqrt{26}$ from the point $P(4,2,7)$ . Then the square of the area of the triangle PQR is ______.

Your answer

Answer and worked solution

Official answer: 153

Foot of the perpendicular from P on the line: $(-1+2t,-2+3t,1+2t)$ with $t=2$ gives $M=(3,4,5)$ , $PM^2=1+4+4=9$ .

Half-base. $QM^2=26-9=17$ .

Area² $=(QM\cdot PM)^2=17\times9=153$ .

Answer: 153

Topics:Angles and distances Equation of a line in space

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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 30