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

MathematicsSingle correct+4 / -1Question 14 of 90

The shortest distance between the lines $\dfrac{x-3}2=\dfrac{y-2}3=\dfrac{z-1}{-1}$ and $\dfrac{x+3}2=\dfrac{y-6}1=\dfrac{z-5}3$ , is

\dfrac{18}{\sqrt5}

\dfrac{22}{3\sqrt5}

\dfrac{46}{3\sqrt5}

6\sqrt3

Answer and worked solution

Official answer: A

Data. $\vec a_2-\vec a_1=(-6,4,4)$ , $\vec d_1\times\vec d_2=(2,3,-1)\times(2,1,3)=(10,-8,-4)$ .

Distance. $\dfrac{|-60-32-16|}{\sqrt{180}}=\dfrac{108}{6\sqrt5}=\dfrac{18}{\sqrt5}$ .

(A)

Topics:Skew lines Cross product

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