🔥 One shot Revision: Lines Class 12 Maths! ⏱️ 8 minutes Masterclass

Описание: PYQ+FORMULA PDF:
https://drive.google.com/file/d/17S6M...


This video provides a one-shot revision for the "Lines" chapter in Class 12 Maths, focusing on key formulas and previously asked questions (PYQs) from HSC 2018-2025, which is helpful for HSC 2026 boards and MHT-CET preparation.

The video covers the following main points:
• Equation of a line: The basic equation of a line is introduced as `r = a + λb`, where `a` is the position vector of a point the line passes through, and `b` is analogous to the slope in 2D, representing the direction ratios in 3D (0:07).
• Angle between lines and planes: The formula for the angle between two lines or two planes is `cos θ` (0:46). However, for the angle between a plane and a line, `sin θ` is used (0:53).

rection ratios: The video explains how to extract direction ratios (`a1, b1, c1` and `a2, b2, c2`) from given equations of lines for use in angle formulas (1:03).
• Cartesian equation of a line: The Cartesian form `(x - x1)/a = (y - y1)/b = (z - z1)/c` is discussed for a line passing through a point and having direction ratios (1:37).
• Vector equation of a line:
• Passing through a point and parallel to a vector: If a line passes through a point with position vector `a` and is parallel to vector `b`, its equation is `r = a + λb` (1:56).
• Passing through two points (A and B): The formula `r = a + λ(b - a)` is provided for a line passing through points A and B (4:00).
• Line perpendicular to vectors: The concept of a line passing through a point and being perpendicular to two vectors (say, `b` and `c`) involves using the cross product `b × c` to find the direction vector of the line (3:11).
• Simplifying direction ratios: The video demonstrates how to simplify direction ratios when they are in fractional form by multiplying them by a common multiple (5:30).
• Condition for intersecting lines: Lines intersect if the determinant of a specific matrix formed by the coordinates of points and direction ratios is zero (6:05).
• Special cases for direction ratios: For equations like `z = -1`, the direction ratio `c` becomes zero (7:06).
• Right angles between lines: The condition for lines being at right angles can be found using the `cos θ` formula (7:16).

The video also mentions providing a PDF with PYQs and formulas for further practice (2:26, 7:26).

Quick revision of Lines for Class 12 Maths! 📚 All concepts, one shot! #MathsRevision #Class12
🔥 Complete One Shot Revision for LINE chapter (Class 12 Maths - Line & Plane)! Master all formulas (general form, parametric, point-slope), distance formulas, angle between lines/planes, plus solved PYQs from HSC 2018-2025. Perfect for HSC 2026 boards & MHT-CET prep.

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