The angle subtended at the point (1, 2, 3) by the points P(2, 4,

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 Multiple Choice QuestionsMultiple Choice Questions

161.

The plane x + 3y + 13 = 0 passes through the line of intersection of the planes 2x - 8y + 4z = p and 3x - 5y + 4z + 10 = 0. If the plane is perpendicular to the plane 3x - y - 2z - 4 = 0, then the value of p is

  • 2

  • 5

  • 9

  • 3


162.

If a straight line makes the angles 60°, 45° and α with X, Y and Z-axes respectively, then sin2α is equal to

  • 34

  • 32

  • 12

  • 1


163.

The angle between a and b is 5π6 and  and the projection of a on b is - 93, then a is equal to

  • 12

  • 8

  • 10

  • 6


164.

The direction cosines of the straight line given by the planes x = 0 and z = 0 are

  • 1, 0, 0

  • 0, 0, 1

  • 1, 1, 0

  • 0, 1, 0


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165.

If a . b = 0 and a + b makes an angle of 60° with b, then a is equal to

  • 0

  • 13b

  • 1b

  • 3b


166.

The straight line r = (i^ + j^ + k^) + a(2i^ - j^ + 4k^) meets the XY - plane at the point

  • (2, - 1, 0)

  • (3, 4, 0)

  • 12, 34, 0

  • 12, 54, 0


167.

The equation of the plane passing through (- 1, 5, - 7) and parallel to the plane 2x - 5y + 7z + 11 = 0, is

  • r. 2i^ - 5j^ - 7k^ + 76 = 0

  • r. 2i^ - 5j^ + 7k^ + 76 = 0

  • r. 2i^ - 5j^ -+ 7k^ + 75 = 0

  • r. 2i^ - 5j^ + 7k^ + 65 = 0


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168.

The angle subtended at the point (1, 2, 3) by the points P(2, 4, 5) and Q(3, 3, 1) is

  • 90°

  • 60°

  • 30°


A.

90°

Given, points

A(1, 2, 3), P(2, 4, 5) and 0(3, 3, 1).

       a = 3 - 1i^ + 3 - 2j^ + 1 - 3k^ = 2i^ + j^ - 2k^and b = 2 - 1i^ + 4 - 2j^ + 5 - 3k^ = i^ + 2j^ + 2k^Let the angle between a and b is θ      cosθ = a . bab = 2i^ + j^ - 2k^i^ + 2j^ + 2k^4 + 1 + 41 + 4 + 9 cosθ = 2 + 2 - 49 = 0 cosθ = cos90°  θ = 90°


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169.

If the two lines x - 12 = 1 - y- a = z4 and x - 31 = 2y - 34 = z - 22 are perpendicular, then the value of a is equal to

  • - 4

  • 5

  • - 5

  • 4


170.

If the line x + 12 = y + 13 = z + 14 meets the plane x + 2y + 3z = 14 at P, then the distance between P and the origin is

  • 14

  • 15

  • 13

  • 12


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