The equation of the bisector of the acute angles between the line

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 Multiple Choice QuestionsMultiple Choice Questions

621.

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

  • 90°

  • 30°

  • 45°


622.

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

  • 26

  • 13

  • 12

  • None of these


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623.

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


C.

21x + 77y - 101 = 0

Given lines are 3x - 4y + 7 = 0or y = 34x + 74              ...iand 12x + 5y - 2 =0or y = - 125x + 25      ...iiThe equation of the bisectors of the angles between these lines are3x - 4y + 732 + 42 = ± 12x + 5y - 2122 + 52 Required equation of the bisector of the acute angle between these lines is3x - 4y + 75 = 12x + 5y - 213   39x - 52y + 91 = 60x + 25y - 10 21x + 77y - 101 = 0


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624.

The angle between the lines in

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

  • 60°

  • 45°

  • 30°

  • 90°


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625.

If the vectors 3i^ + j^ - 2k^i^ + 2j^ - 3k^3i^ + λj^ + 5k^ are co-planar, the value of λ is

  • - 4

  • 4

  • 8

  • - 8


626.

A space vector makes the angles 150° and 60° with the positive direction of x-and y-axes. The angle made by the vector with the positive direction z-axis is

  • 90°

  • 60°

  • 180°

  • 120°


627.

If a, b and c are non-coplanar, then the value of a . b × c3b . c × a - b . c × a2c . a × b is

  • - 12

  • - 13

  • - 16

  • 16


628.

If sin-1a is the acute angle between the curves : x2 + y2 = 4x and x2 + y2 = 8 at (2, 2), then a is equal to

  • 1

  • 0

  • 12

  • 32


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629.

The distance of the point P(a, b, c) from the x-axis is

  • a2 + b2

  • b2 + c2

  • a

  • a2 + c2


630.

Equation of the plane perpendicular to the line x1 = y2 = z3 and passing through the point (2, 3, 4) is

  • 2x + 3y + z = 17

  • x + 2y + 3z = 9

  • 3x + 2y + z = 16

  • x + 2y + 3z = 20


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