JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q83

MathematicsSingle correct+4 / -1Question 83 of 90

Equation of the line of the shortest distance between the lines $\dfrac x1=\dfrac y{-1}=\dfrac z1$ and $\dfrac{x-1}0=\dfrac{y+1}{-2}=\dfrac z1$ is :

\dfrac x1=\dfrac y{-1}=\dfrac z{-2}

\dfrac{x-1}1=\dfrac{y+1}{-1}=\dfrac z{-2}

\dfrac{x-1}1=\dfrac{y+1}{-1}=\dfrac z1

\dfrac x{-2}=\dfrac y1=\dfrac z2

Answer and worked solution

Official answer: B

Points: $P=(t,-t,t)$ and $Q=(1,-1-2s,s)$ . $\vec{PQ}$ must be perpendicular to both directions:

So $s=0$ , $t=\frac23$ , and $Q=(1,-1,0)$ . $\vec{PQ}=\frac13(1,-1,-2)$ , so
$\frac{x-1}1=\frac{y+1}{-1}=\frac z{-2}.$

JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 83