JEE 2023 — Mathematics PYQ

Q: How do I solve JEE 2023 Mathematics questions?

Practice JEE 2023 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of JEE Mathematics questions?

JEE Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are JEE previous year papers available for free?

Yes. Mathem Solvex provides free access to JEE previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The shortest distance between the lines $\frac{x + 2}{1} = \frac{y}{- 2} = \frac{z - 5}{2}$ and $\frac{x - 4}{1} = \frac{y - 1}{2} = \frac{z + 3}{0}$ is:

Choose the correct answer:

Explanation

By using the formula of shortest distance

$d = \frac{a _{2} - a _{1} l _{1} l _{2} am p ; b _{2} - b _{1} am p ; m _{1} am p ; m _{2} am p ; c _{2} - c _{1} am p ; n _{1} am p ; n _{2}}{<} b r > \hat{i} l_{1} l_{2} am p; \hat{j} am p; m_{1} am p; m_{2} am p; \hat{k} am p; n_{1} am p; n_{2}$

We get

$d = \frac{4 + 2 1 1 am p ; 1 - 0 am p ; - 2 am p ; 2 am p ; - 3 - 5 am p ; 2 am p ; 0}{<} b r > \hat{i} 11 am p; \hat{j} am p; - 2 am p; 2 am p; \hat{k} am p; 2 am p; 0$

$\Rightarrow d = \frac{∣6 ( 0 - 4 ) - 1 ( 0 - 2 ) - 8 ( 2 + 2 ) ∣}{<} b r > \hat{i} (0 - 4) - \hat{j} (0 - 2) + \hat{k} (2 + 2)$

$= \frac{∣ - 54∣}{16 + 4 + 16}$

$\Rightarrow d = \frac{54}{6} = 9$