Ex 11.2, 2 - Show line (1, -1, 2), (3, 4, -2) is perpendicular - Angle between two lines - Direction ratios or cosines

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  1. Chapter 11 Class 12 Three Dimensional Geometry
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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.

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  • Sidharth Gat's image

    (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

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  • Sidharth Gat's image

    (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

    View answer
  • Sidharth Gat's image

    (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 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

    View answer
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