JEE Main 2022 · 26 Jul · Shift 1 · Mathematics Q14

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MathematicsSingle correct+4 / -1Question 14 of 90

The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the line $x+y-z=0=x-2y+3z-5$ is :

\sqrt{\dfrac{21}2}

\sqrt{\dfrac92}

\sqrt{\dfrac{73}2}

Answer and worked solution

Official answer: A

Direction $(1,1,-1)\times(1,-2,3)=(1,-4,-3)$ .

Distance of $(1,-2,5)$ from the line through $(1,2,4)$ : $\dfrac{|(0,-4,1)\times(1,-4,-3)|}{\sqrt{26}}=\dfrac{|(16,1,4)|}{\sqrt{26}}=\sqrt{\frac{273}{26}}=\sqrt{\frac{21}2}$ .

(A)

Topics:Angles and distances Equation of a line in space

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JEE Main 2022 · 26 Jul · Shift 1, Mathematics question 14