JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q83

MathematicsSingle correct+4 / -1Question 83 of 90

If the points $(1,1,\lambda)$ and $(-3,0,1)$ are equidistant from the plane, $3x+4y-12z+13=0$ , then λ satisfies the equation :

3x^2-10x+7=0

3x^2+10x+7=0

3x^2+10x-13=0

3x^2-10x+21=0

Answer and worked solution

Official answer: A

$|3+4-12\lambda+13|=|-9+0-12+13|=8$ , so $|20-12\lambda|=8$ and $\lambda=1$ or $\frac73$ . Both satisfy $3x^2-10x+7=0$ .

JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 83