JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q83

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MathematicsSingle correct+4 / -1Question 83 of 90

The shortest distance between the $z$ -axis and the line $x+y+2z-3=0=2x+3y+4z-4$ , is :

Answer and worked solution

Official answer: B

The line has direction $(1,1,2)\times(2,3,4)=(-2,0,1)$ and passes through $(5,-2,0)$ . With the $z$ -axis, the common normal is $(-2,0,1)\times(0,0,1)=(0,2,0)$ :
$d=\frac{|(5,-2,0)\cdot(0,2,0)|}2=2.$

Topics:Skew lines

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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 83