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Ex 11.3
Ex 11.3, 1 (b)
Ex 11.3, 1 (c) Important
Ex 11.3, 1 (d) Important
Ex 11.3, 2
Ex 11.3, 3 (a)
Ex 11.3, 3 (b)
Ex 11.3, 3 (c) Important
Ex 11.3, 4 (a) Important
Ex 11.3, 4 (b)
Ex 11.3, 4 (c)
Ex 11.3, 4 (d) Important
Ex 11.3, 5 (a) Important
Ex 11.3, 5 (b)
Ex 11.3, 6 (a) Important
Ex 11.3, 6 (b) You are here
Ex 11.3, 7
Ex 11.3, 8
Ex 11.3, 9
Ex 11.3, 10 Important
Ex 11.3, 11 Important
Ex 11.3, 12 Important
Ex 11.3, 13 (a) Important
Ex 11.3, 13 (b) Important
Ex 11.3, 13 (c)
Ex 11.3, 13 (d)
Ex 11.3, 13 (e)
Ex 11.3, 14 (a) Important
Ex 11.3, 14 (b)
Ex 11.3, 14 (c)
Ex 11.3, 14 (d) Important
Last updated at Aug. 24, 2021 by Teachoo
Ex 11.3, 6 Find the equations of the planes that passes through three points. (b) (1, 1, 0), (1, 2, 1), (β2, 2, β1) Vector equation of a plane passing through three points with position vectors π β, π β, π β is ("r" β β π β) . [(π ββπ β)Γ(π β βπ β)] = 0 Now, the plane passes through the points A (1, 1, 0) π β = 1π Μ + 1π Μ + 0π Μ B (1, 2, 1) π β = 1π Μ + 2π Μ + 1π Μ C (β2, 2, β1) π β = β2π Μ + 2π Μ β 1π Μ (π β β π β) = (1π Μ + 2π Μ + 1π Μ) β (1π Μ + 1π Μ + 0π Μ) = (1 β 1) π Μ + (2 β 1)π Μ + (1 β 0) π Μ = 0π Μ + 1π Μ + 1π Μ (π β β π β) = (β2π Μ + 2π Μ + 1π Μ) β (1π Μ + 1π Μ +0π Μ) = (β2 β 1)π Μ + (2 β 1)π Μ + (β1 β 0) π Μ = β3π Μ + 1π Μ β 1π Μ (π β β π β) Γ (π β β π β) = |β 8(π Μ&π Μ&π Μ@0&1&1@ β 3&1& β 1)| = π Μ [(1Γβ1)β(1Γ1)] β π Μ [(0Γβ1)β(β3 Γ1)] + (π ) Μ[(0Γ1)β(β3 Γ1)] = π Μ(β1 β 1) β π Μ (0 + 3) + π Μ ( 0 + 3) = β2π Μ β 3π Μ + 3π Μ β΄ Vector equation of plane is [π ββ(1π Μ+1π Μ+0π Μ ) ].(β2π Μβ3π Μ+3π Μ ) = 0 [π ββ(π Μ+π Μ ) ].(βππ Μβππ Μ+ππ Μ ) = π Finding Cartesian equation Put π β = xπ Μ + yπ Μ + zπ Μ [π ββ(π Μ+π Μ ) ].(β2π Μβ3π Μ+3π Μ ) = 0 [(π₯π Μ+π¦π Μ+π§π Μ )β(π Μ+π Μ)]. (β2π Μβ3π Μ+3π Μ ) = 0 [(π₯β1) π Μ +(π¦β1) π Μ+π§π Μ ]. (β2π Μβ3π Μ+3π Μ ) = 0 β2(x β 1) + (β3)(y β 1) + 3(z) = 0 β2x + 2 β 3y + 3 + 3z = 0 2x + 3y β 3z = 5 β΄ Equation of plane in Cartesian form is 2x + 3y β 3z = 5