Ex 11.2, 2
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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(https://www.teachoo.com/3504/753/Ex-11.2--2---Show-line-(1---1--2)--(3--4---2)-is-perpendicular/category/Ex-11.2/)
But 1st we need to prove that lines are intersecting one's coz in 3d we have skew lines for which angle between lines has no meaning as it can't be found coz they don't intersect
(https://www.teachoo.com/3504/753/Ex-11.2--2---Show-line-(1---1--2)--(3--4---2)-is-perpendicular/category/Ex-11.2/)
But 1st we need to prove that lines are intersecting one's coz in 3d we have skew lines for which angle between lines has no meaning as it can't be found coz they don't intersect