Three Dimensional Geometry

1

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line, x/1 = y/4 = z/5 is Q, then PQ is equal to:

  1. 3√5
  2. 2√42
  3. √42
  4. 6√5
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2

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l2 + m2 + n2 = 0 is

  1. π/2
  2. π/3
  3. π/4
  4. π/6
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3

If the lines (x - 1)/2 = (y + 1)/2 = (z - 1)/4 and (x - 3)/1 = (y - k)/2 = z/1 intersect, then k is equal to

  1. 9/2
  2. 2/9
  3. -1
  4. 0
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4

If the angle between the line x = (y - 1)/2 = (z - 3)/λ and the plane x + 2y + 3z = 4 is cos-1(5/14) then λ is equal to

  1. 3/2
  2. 2/5
  3. 2/3
  4. 5/3
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5

A line AB in three-dimensional space makes angles 45° and 120° with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle θ with the positive z-axis, then θ equals

  1. 30°
  2. 45°
  3. 60°
  4. 75°
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6

Let the line (x - 2)/3 =  (y - 1)/-5 =  (z - 2)/2 lie in the plane x + 3y - αz + β = 0. Then (α, β) equals

  1. (-5, 5)
  2. (5, -15)
  3. (-6, 7)
  4. (6, -17)
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7

The distance of the point (1,0,2) from the point of intersection of the line (x - 2)/3 = (y + 1)/4 = (z - 2)/12 and the plane x - y + z = 16 is 

  1. 13
  2. 8
  3. 3√21
  4. 2√14
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8

A plane which passes through the point (3, 2, 0) and the line (x-4)/1 = (y-7)/5 = (z-4)/4 is

  1. 2x - y + z = 5
  2. x + 2y - z = 1
  3. x - y + z = 1
  4. x + y + z = 5
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9

If the line, (x-3)/2 = (y+2)/-1 = (z+4)/3, lies in the plane, lx + my – z = 9, then l2 + m2 is equal to:

  1. 18
  2. 5
  3. 2
  4. 26
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