Last updated at Jan. 3, 2020 by Teachoo

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Misc 19 (Method 1) Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes . ( + 2 ) = 5 and . (3 + + ) = 6 . The vector equation of a line passing through a point with position vector and parallel to a vector is = + Given, the line passes through (1, 2, 3) So, = 1 + 2 + 3 Given, line is parallel to both planes Line is perpendicular to normal of both planes. i.e. is perpendicular to normal of both planes. We know that is perpendicular to both & So, is cross product of normals of planes . ( + 2 ) = 5 and . (3 + + ) = 6 Required normal = 1 1 2 3 1 1 = ( 1(1) 1(2)) (1(1) 3(2)) + (1(1) 3( 1)) = ( 1 2) (1 6) + (1 + 3) = 3 + 5 + 4 Thus, = 3 + 5 + 4 Now, Putting value of & in formula = + = ( + 2 + 3 ) + ( 3 + 5 + 4 ) Therefore, the equation of the line is ( + 2 + 3 ) + ( 3 + 5 + 4 ). Misc 19 (Method 2) Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes . ( + 2 ) = 5 and . (3 + + ) = 6 . The vector equation of a line passing through a point with position vector and parallel to a vector is = + Given, the line passes through (1, 2, 3) So, = 1 + 2 + 3 Let = 1 + 2 + 3 A line parallel to a plane is perpendicular to the normal of the plane. And two lines and are perpendicular if . = 0 Given, the line is parallel to planes So, our equations are 1 2 + 2 3 = 0 3 1 + 2 + 3 = 0 Thus, = 1 + 2 + 3 = 3k + 5k + 4k Now, Putting value of & in formula = + = (1 + 2 + 3 ) + ( 3k + 5k + 4k ) = ( + 2 + 3 ) + k ( 3 + 5 + 4 ) = ( + 2 + 3 ) + ( 3 + 5 + 4 ) Therefore, the equation of the line is ( + 2 + 3 ) + ( 3 + 5 + 4 ).

Miscellaneous

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Misc 2

Misc 3

Misc 4 Important

Misc 5 Important

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18 Important

Misc 19 Important You are here

Misc 20 Important

Misc 21 Important

Misc 22 Important

Misc 23 Important

Chapter 11 Class 12 Three Dimensional Geometry

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.