The distance of the point from the plane parallel to the line of the shortest distance between the lines and is:

Explanation: 1. Shortest Distance (S.D.) ki direction nikalna S.D. hamesha dono lines ke perpendicular hoti hai. Agar lines ki directions aur hain, toh S.D. ki direction hogi. Direction ( ): 2. Point se guzarne wali line ki equation Hume is point se ek line draw karni hai jo ke parallel ho: Is line par koi bhi general point hoga: . 3. Plane ke saath intersection point nikalna Plane ki equation Cartesian form mein: . Point ko plane ki equation mein rakhne par: Intersection point ke coordinates: Toh point . 4. Distance calculate karna Ab point aur ke beech ki distance: Correct Answer Sahi option (4) hai.

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

The distance of the point $(-1, 2, 3)$ from the plane $\vec{r} \cdot (\hat{i} - 2\hat{j} + 3\hat{k}) = 10$ parallel to the line of the shortest distance between the lines $\vec{r} = (\hat{i} - \hat{j}) + \lambda(2\hat{i} + \hat{k})$ and $\vec{r} = (2\hat{i} - \hat{j}) + \mu(\hat{i} - \hat{j} + \hat{k})$ is:

JEE 2023 — Mathematics PYQ

Choose the correct answer:

Explanation

1. Shortest Distance (S.D.) ki direction nikalna

2. Point $(-1, 2, 3)$ se guzarne wali line ki equation

3. Plane ke saath intersection point nikalna

4. Distance calculate karna

Correct Answer