JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q22

← JEE Main 2022 · 26 Jul · Shift 2

MathematicsInteger+4 / -1Question 22 of 90

The largest value of $a$ , for which the perpendicular distance of the plane containing the lines $\vec r=\left(\hat i+\hat j\right)+\lambda\left(\hat i+a\hat j-\hat k\right)$ and $\vec r=\left(\hat i+\hat j\right)+\mu\left(-\hat i+\hat j-a\hat k\right)$ from the point $(2,1,4)$ is $\sqrt3$ , is ______.

Your answer

Answer and worked solution

Official answer: 2

Plane. Both lines pass through $(1,1,0)$ ; normal $(\hat i+a\hat j-\hat k)\times(-\hat i+\hat j-a\hat k)=(a+1)(1-a,1,1)$ .

Distance. $\frac{|(1-a)+0+4|}{\sqrt{(1-a)^2+2}}=\sqrt3$ gives $a^2+2a-8=0$ : $a=2$ or $-4$ .

Answer: 2

Topics:Equation of a plane Angles and distances

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JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 22