Ex 11.2

Chapter 11 Class 12 Three Dimensional Geometry
Serial order wise

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Question 1 Find the vector and the Cartesian equations of the line that passes through the points (3, β 2, β 5), (3, β 2, 6).Vector Equation Vector equation of a line passing through two points with position vectors π β and π β is π β = π β + π (π β β π β) Given, the two points are So, π β = (3π Μ β 2π Μ β 5π Μ) + π ["(3" π Μβ"2" π Μ+"6" π Μ")" β"(3" π Μβ"2" π Μ β"5" π Μ")" ] = 3π Μ β 2π Μ β 5π Μ + π ["(3" β3")" π Μβ"(2" β(β2))π Μ+(6β(β5))π Μ)] A (3, β 2, β 5) π β = 3π Μ β 2π Μ β 5π Μ B (3, β 2, 6) π β = 3π Μ β 2π Μ + 6π Μ = 3π Μ β 2π Μ β 5π Μ + π [0π Μ + 0π Μ + 11π Μ] = 3π Μ β 2π Μ β 5π Μ + π (11π Μ) Therefore, the vector equation is π β = 3π Μ β 2π Μ β 5π Μ + π (11π Μ) Cartesian equation Cartesian equation of a line passing through two points A(x1, y1, z1) and B (x2, y2, z2) is (π₯ β π₯1)/(π₯2 β π₯_1 ) = (π¦ β π¦1)/(π¦2 β π¦1) = (π§ β π§1)/(π§2 β π§1) Since the line passes through A (3, β2, β5) x1 = 3, y1 = β2, z1 = β 5 And also passes through B (3, β2, 6) x2 = 3, y2 = β2, z2 = 6 Equation of line is (π₯ β 3)/(3 β 3) = (π¦ β (β2))/( β2 β (β2)) = (π§ β (β5))/(6 β (β5)) (π β π)/π = (π + π)/π = (π + π)/ππ