JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q83

← JEE Main 2017 · 2 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 83 of 90

If the image of the point P(1, −2, 3) in the plane, $2x+3y-4z+22=0$ measured parallel to the line, $\dfrac x1=\dfrac y4=\dfrac z5$ is Q, then PQ is equal to :

2\sqrt{42}

\sqrt{42}

6\sqrt5

3\sqrt5

Answer and worked solution

Official answer: A

The line through P along $(1,4,5)$ meets the plane where $6-6t=0$ , i.e. $t=1$ . The image is at $t=2$ , so
$PQ=2\sqrt{1+16+25}=2\sqrt{42}.$

Topics:Equation of a line in space Equation of a plane

← Previous question Next question →

JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 83