3D Geometry

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JEE Main 2021 (Online) 27th July Evening ShiftQuestion 146

For real numbers $\alpha$ and $\beta\ne0$, if the point of intersection of the straight lines $\frac{x-\alpha}{1}=\frac{y-1}{2}=\frac{z-1}{3}$ and $\frac{x-4}{\beta}=\frac{y-6}{3}=\frac{z-7}{3}$, lies on the plane $x+2y-z=8$, then $\alpha-\beta$ is equal to :

3D Geometry

$3$$5$$7$$9$

JEE Main 2021 (Online) 18th March Morning ShiftQuestion 147

The equation of the planes parallel to the plane $x-2y+2z-3=0$ which are at unit distance from the point $(1,2,3)$ is $ax+by+cz+d=0$. If $(b-d)=K(c-a)$, then the positive value of $K$ is $\_\_\_\_\_\_$ .

3D Geometry

Your answer

JEE Main 2021 (Online) 26th February Morning ShiftQuestion 148

Let $(\lambda,2,1)$ be a point on the plane which passes through the point $(4,-2,2)$. If the plane is perpendicular to the line joining the points $(-2,-21,29)$ and $(-1,-16,23)$, then $\left(\frac{\lambda}{11}\right)^{2}-\frac{4\lambda}{11}-4$ is equal to $\_\_\_\_\_\_$ .

3D Geometry

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JEE Main 2022 (Online) 25th July Morning ShiftQuestion 149

Let $P$ be the plane containing the straight line $\frac{x-3}{9}=\frac{y+4}{-1}=\frac{z-7}{-5}$ and perpendicular to the plane containing the straight lines $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$ and $\frac{x}{3}=\frac{y}{7}=\frac{z}{8}$. If $d$ is the distance of $P$ from the point $(2,-5,11)$, then $d^2$ is equal to :

3D Geometry

$\frac{147}{2}$$96$$\frac{32}{3}$$54$

JEE Main 2021 (Online) 27th July Morning ShiftQuestion 150

Let the plane passing through the point $(-1,0,-2)$ and perpendicular to each of the planes $2x+y-z=2$ and $x-y-z=3$ be $ax+by+cz+8=0$. Then the value of $a+b+c$ is equal to :

3D Geometry

$5$$3$$4$$8$