Ex 11.2, 9 - Chapter 11 Class 12 Three Dimensional Geometry

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Ex 11.2, 9 Find the vector and the Cartesian equations of the line that passes through the points (3, 2, 5), (3, 2, 6). Vector Equation Vector equation of a line passing through two points with position vectors and is = + ( ) Given, the two points are So, = (3 2 5 ) + (3 2 +6 ) (3 2 5 ) = 3 2 5 + (3 3) (2 ( 2)) + (6 ( 5)) ) = 3 2 5 + [0 + 0 + 11 ] = 3 2 5 + (11 ) Therefore, the vector equation is = 3 2 5 + (11 ) Cartesian equation Cartesian equation of a line passing through two points A(x1, y1, z1) and B (x2, y2, z2) is 1 2 1 = 1 2 1 = 1 2 1 Since the line passes through A (3, 2, 5) x1 = 3, y1 = 2, z1 = 5 And also passes through B (3, 2, 6) x2 = 3, y2 = 2, z2 = 6 Equation of line is 3 3 3 = ( 2) 2 ( 2) = ( 5) 6 ( 5) = + = +