The angle between the lines inx2 - xy - 6y2 - 7x + 31y - 18 = 0 i

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 Multiple Choice QuestionsMultiple Choice Questions

281.

The ratio in which the line joining (2, 4, 5), (3, 5, - 4) is divided by the yz-plane is

  • 2 : 3

  • 3 : 2

  • - 2 : 3

  • 4 : - 3


282.

The equation of line of intersection of planes 4x + 4y - 5z = 12, 8x + 12y - 13z = 32can be written as :

  • x - 12 = y + 2- 3 = z4

  • x - 12 = y + 23 = z4

  • x2 = y + 13 = z - 24

  • x2 = y3 = z - 24


283.

The equation of the plane, which makes with co-ordinate axes, a triangle with its centroid α, β, γ is :

  • αx + βy + γz = 3

  • αx + βy + γz = 1

  • xα + yβ + zγ = 3

  • xα + yβ + zγ = 1


284.

A variable plane moves so that sum of the reciprocals of its intercepts on the co-ordinate axes is 1/2. Then the plane passes through :

  • 12, 12, - 12

  • (- 1, 1, 1)

  • (2, 2, 2)

  • (0, 0, 0)


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285.

The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is :

  • π3

  • π4

  • π2

  • 0


286.

The equation of the plane passing through three non-collinear points a, b, c is :

  • r . b × c + c × a + a × b = 0

  • r . b × c + c × a + a × b = a b c

  • r . a × b × c = a b c

  • r . a + b + c = a b c


287.

The angle between the lines 2x = 3y = - z and 6x = - y = -  4z is :

  • 90°

  • 30°

  • 45°


288.

Cosine of the angle between two diagonals of a cube is equal to :

  • 26

  • 13

  • 12

  • None of these


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289.

The equation of the bisector of the acute angles between the lines 3x - 4y + 7=0 and 12x + 5y - 2 = 0 is :

  • 99x - 27y - 81 = 0

  • 11x - 3y + 9 = 0

  • 21x + 77y - 101 = 0

  • 21x + 77y + 101 = 0


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290.

The angle between the lines in

x2 - xy - 6y2 - 7x + 31y - 18 = 0 is

  • 60°

  • 45°

  • 30°

  • 90°


B.

45°

The angle between the lines is given by     tanθ = 2h2 - aba +bHere,   h = - 1/2, a = 1, b = - 6 tanθ = 214 + 61 - 6 = 2254- 5 = - 1        θ = tan-11 = 45°


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