JEE Main 2022 · 27 Jul · Shift 2 · Mathematics Q14

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MathematicsSingle correct+4 / -1Question 14 of 90

If the length of the perpendicular drawn from the point $P(a,4,2)$ , $a>0$ on the line $\dfrac{x+1}2=\dfrac{y-3}3=\dfrac{z-1}{-1}$ is $2\sqrt6$ units and $Q(\alpha_1,\alpha_2,\alpha_3)$ is the image of the point P in this line, then $a+\displaystyle\sum_{i=1}^3\alpha_i$ is equal to :

Answer and worked solution

Official answer: B

Foot. On the line, $(-1+2t,3+3t,1-t)$ with $PM\perp$ the direction gives $t=\frac{a+2}7$ . $|PM|^2=24$ holds at $a=5$ , $t=1$ , so $M=(1,6,0)$ .

Image $Q=2M-P=(-3,8,-2)$ , sum 3. So $a+\sum\alpha_i=8$ .

(B)

Topics:Angles and distances Equation of a line in space

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JEE Main 2022 · 27 Jul · Shift 2, Mathematics question 14