JEE Main 2016 · 3 Apr · Shift 1 · Mathematics Q84

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MathematicsSingle correct+4 / -1Question 84 of 90

If the line, $\dfrac{x-3}2=\dfrac{y+2}{-1}=\dfrac{z+4}3$ lies in the plane, $lx+my-z=9$ , then $l^2+m^2$ is equal to :

Answer and worked solution

Official answer: D

The line lies in the plane, so its direction (2, −1, 3) is perpendicular to the normal: $2l-m-3=0$ . The point (3, −2, −4) is on the plane: $3l-2m+4=9$ . So $l=1$ , $m=-1$ and $l^2+m^2=2$ .

Topics:Equation of a plane

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JEE Main 2016 · 3 Apr · Shift 1, Mathematics question 84