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QJEEM23Ma50bd: JEE Main 2023 Mathematics - Class 12 JEEM23Ma50bd Solution: The distance of the point P(4, 6, − 2) from the line passing…

The distance of the point P(4, 6, −2) from the line passing through the point (−3, 2, 3) and parallel to a line with direction ratios 3, 3, −1 is equal to :

Multiple Choice Options

  • A 3
  • B 14
  • C 6
  • D 23

Step-by-Step Verified Solution

JEE Main 2023 (Online) 25th January Morning Shift Mathematics - 3D Geometry Question 105 English Explanation

AP→=7i^+4j^−5k^⇒∣AP→∣=49+16+25=90AN\overrightarrow{A P}=7 \hat{i}+4 \hat{j}-5 \hat{k} \Rightarrow|\overrightarrow{A P}|=\sqrt{49+16+25}=\sqrt{90} A N

== projection of AP→\overrightarrow{A P} on b⃗=AP→⋅b⃗=21+12+519=3819\vec{b}=\overrightarrow{A P} \cdot \vec{b}=\frac{21+12+5}{\sqrt{19}}=\frac{38}{\sqrt{19}}

(PN)2=(AP)2−(AN)2=90−76=14⇒PN=14(P N)^{2}=(A P)^{2}-(A N)^{2}=90-76=14 \Rightarrow P N=\sqrt{14}

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