Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 11.2, 2 Show that the line through the points (1, −1, 2), (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6). Two lines with direction ratios 𝑎1, 𝑏1, 𝑐1 and 𝑎2, 𝑏2, 𝑐2 are perpendicular to each other if 𝒂𝟏 𝒂𝟐 + 𝒃𝟏 𝒃𝟐 + 𝒄𝟏 𝒄𝟐 = 0 Now, a line passing through (x1, y1, z1) and (x2, y2, z2) has the direction ratios (x2 − x1), (y2 − y1), (z2 − z1) Now, 𝑎1 𝑎2 + 𝑏1 𝑏2 + 𝑐1 𝑐2 = (2 × 3) + (5 × 2) + ( − 4 × 4) = 6 + 10 + (− 16) = 16 − 16 = 0 Therefore the given two lines are perpendicular.

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

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