If a straight line makes angles α, β, &gamma

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 Multiple Choice QuestionsMultiple Choice Questions

151.

Equation of the line through the point (2, 3, 1) and parallel to the line of intersection of the planes x - 2y - z + 5 = 0 and x + y + 3z = 6 is

  • x - 2- 5 = y - 3- 4 = z - 13

  • x - 25 = y - 3- 4 = z - 13

  • x - 25 = y - 3- 4 = z - 13

  • x - 24 = y - 34 = z - 12


152.

The angle between a normal to the plane 2x - y + 2z - 1 = 0 and the Z-axis is

  • cos-113

  • sin-123

  • cos-123

  • sin-113


153.

Foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z = 29 is

  • (5, - 1, 4)

  • (7, - 1, 3)

  • (5, - 2, 3)

  • (2, - 3, 4)


154.

The distance between the X-axis and the point (3, 12, 5) is

  • 3

  • 13

  • 14

  • 12


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155.

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

  • π6

  • π4

  • π3

  • π2


156.

The projection of the line segment joining (2, 0, - 3) and (5, - 1, 2) on a straight line whose direction ratios are 2, 4, 4, is

  • 116

  • 103

  • 133

  • 113


157.

The angle between the straight line r = i^ + 2j^ + k^ + i^ - j^ + k^ and the plane r . 2i^ - j^ + k^ = 4 is

  • sin-1223

  • sin-126

  • sin-123

  • sin-123


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158.

If a straight line makes angles α, β, γ with the coordinate axes, then 1 - tan2α1 - tan2α + 1sec2β - 2sin2γ is equal to

  • - 1

  • 1

  • - 2

  • 2


C.

- 2

If a straight line makes angles α, β, γ with the coordinate axes.

Then, cos2α + cos2β + cos2γ = 1 1 + cos2α2 + 1 + cos2β2 + 1 - sin2γ = 1  1 + cos2α + 1 + cos2β + 2 - 2sin2γ = 2           cos2α + cos2β - 2sin2γ = - 2 1 - tan2α1 + tan2α + 1sec2β - 2sin2γ = - 2


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159.

The equation of the plane which bisects the· line segment joining the points (3, 2, 6) and (5, 4, 8) and is perpendicular to the same line segment, is

  • x + y + z = 16

  • x + y + z = 10

  • x + y + z = 12

  • x + y + z = 14


160.

The foot of the perpendicular from the point (1, 6, 3) to the line x1 = y - 12 = z - 23 is

  • (1, 3, 5)

  • (- 1, - 1, - 1)

  • (2, 5, 8)

  • (- 2, - 3, - 4)


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