Find the area of the triangle whose vertices are (1, 2, 4), (-2, 1, 2), (2, 4, -3).
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Long Answer Type
102.A line makes angle α, β, γ and δ with the diagonals of a cube, prove that
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103.If the edges of a rectangular parallelepiped are a, b, c, show that the angles between four diagonals are given by cos–1
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104.Find the angle between two diagonals of a cube.
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105.Show that the line joining the middle points of two sides of a triangle is parallel to the third side and half of it in length.
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106.A variable line in two adjacent positions has direction cosines < l, m, n > and < l + δl, m + δm, n + δn >. Show that the small angle δθ between two positions is given by (δθ )2 = (δl)2 + (δm)2 + (δn)2
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107.
Find the angle between the two lines whose direction cosines are given by the equations: l + m + n = 0, l2 + m2 – n2 = 0
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108.Find the angle between the two lines whose direction cosines are given by the equations: 2 l – m + 2 n = 0 and m n + n l + l m = 0
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109.Find the angle between the two lines whose direction cosines are given by the equations: l + m + n = 0 and 2 l + 2 m – m n = 0
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110.Show that the straight lines whose direction cosines are given by the equations uI + vm + wn = 0, a I2 + b m2 + cn2 = 0 are (i) perpendicular if u2 (b + c) + v2 (c + a) + w2 (a + b) = 0 (ii) parallel if
Short Answer Type
Long Answer Type
