JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q9

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MathematicsSingle correct+4 / -1Question 9 of 90

If the foot of the perpendicular from the point A(−1, 4, 3) on the plane P : $2x+my+nz=4$ , is $\left(-2,\dfrac72,\dfrac32\right)$ , then the distance of the point A from the plane P, measured parallel to a line with direction ratios 3, −1, −4, is equal to :

\sqrt{26}

2\sqrt2

\sqrt{14}

Answer and worked solution

Official answer: B

Normal. $A-\text{foot}=\left(1,\frac12,\frac32\right)\parallel(2,1,3)$ , so $m=1$ , $n=3$ .

Line $(-1+3t,\,4-t,\,3-4t)$ meets $2x+y+3z=4$ when $11-7t=4$ , $t=1$ . Distance $\sqrt{9+1+16}=\sqrt{26}$ .

(B)

Topics:Angles and distances Equation of a plane

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JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 9