JEE Main 2023 (Online) 15th April Morning Shift | 3D Geometry Question 46 | Mathematics

Let $\mathrm{S}$ be the set of all values of $\lambda$, for which the shortest distance between

the lines $\frac{x-\lambda}{0}=\frac{y-3}{4}=\frac{z+6}{1}$ and $\frac{x+\lambda}{3}=\frac{y}{-4}=\frac{z-6}{0}$ is 13. Then $8\left|\sum\limits_{\lambda \in S} \lambda\right|$ is equal to :

306

304

308

302

JEE Main 2023 (Online) 13th April Evening Shift

MCQ (Single Correct Answer)

-1

The line, that is coplanar to the line $$\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$$, is :

$$\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{4}$$

$$\frac{x+1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$$

$$\frac{x-1}{-1}=\frac{y-2}{2}=\frac{z-5}{5}$$

$$\frac{x+1}{1}=\frac{y-2}{2}=\frac{z-5}{5}$$

JEE Main 2023 (Online) 13th April Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

The plane, passing through the points $$(0,-1,2)$$ and $$(-1,2,1)$$ and parallel to the line passing through $$(5,1,-7)$$ and $$(1,-1,-1)$$, also passes through the point :

$$(0,5,-2)$$

$$(2,0,1)$$

$$(1,-2,1)$$

$$(-2,5,0)$$

JEE Main 2023 (Online) 13th April Evening Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Let $$\mathrm{N}$$ be the foot of perpendicular from the point $$\mathrm{P}(1,-2,3)$$ on the line passing through the points $$(4,5,8)$$ and $$(1,-7,5)$$. Then the distance of $$N$$ from the plane $$2 x-2 y+z+5=0$$ is :