Important Questions of Three Dimensional Geometry Mathematics | Zigya

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11.

If the angle between the line x =fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 3 over denominator straight lambda end fraction and the plane x + 2y + 3z = 4 is cos-1 square root of 5 over 14 end root then λ equal

  • 2/3

  • 3/2

  • 2/5

  • 2/5

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12.

Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line: straight x over 1 space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 2 over denominator 3 end fraction
Statement-2: The line:straight x over 1 space equals space fraction numerator straight y minus 1 over denominator 2 end fraction space equals space fraction numerator straight z minus 2 over denominator 3 end fraction  bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).

  • Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1. 

  • Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. 

  • Statement-1 is true, Statement-2 is false.

  • Statement-1 is true, Statement-2 is false.

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13.

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

  • 30°

  • 45°

  • 60°

  • 60°

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14.

The line L given by straight x over 5 space plus straight y over straight b space equals space 1 passes through the point (13, 32). The line K is parallel to L and has the equation straight x over straight c space plus straight y over 3 space equals space 1 . Then the distance
between L and K is

  • fraction numerator 23 over denominator square root of 15 end fraction
  • square root of 17
  • fraction numerator 17 over denominator square root of 15 end fraction
  • fraction numerator 17 over denominator square root of 15 end fraction
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15.

Let k be an integer such that triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point 

  • open parentheses 2 comma 1 half close parentheses
  • open parentheses 2 comma negative 1 half close parentheses
  • open parentheses 1 comma negative 3 over 2 close parentheses
  • open parentheses 1 comma negative 3 over 2 close parentheses
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16.

The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the point

  • open parentheses fraction numerator 1 over denominator 2 comma end fraction 1 third close parentheses
  • open parentheses fraction numerator 1 over denominator 2 comma end fraction 1 half close parentheses
  • open parentheses fraction numerator 1 over denominator 2 comma end fraction 1 half close parentheses
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17.

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

  • 6 square root of 7
  • 3 square root of 5
  • 2 square root of 42
  • 2 square root of 42
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18.

The distance of the point (1, 3, –7) from the plane passing through the point (1, –1, –1), having normal perpendicular to both the linesfraction numerator straight x minus 1 over denominator 1 end fraction space equals space fraction numerator straight y plus 2 over denominator negative 2 end fraction space equals space fraction numerator straight z minus 4 over denominator 3 end fraction space and space fraction numerator straight x minus 2 over denominator 2 end fraction space equals space fraction numerator straight y plus 1 over denominator negative 1 end fraction space equals space fraction numerator straight z plus 7 over denominator negative 1 end fraction is

  • fraction numerator 10 over denominator square root of 74 end fraction
  • fraction numerator 20 over denominator square root of 74 end fraction
  • fraction numerator 10 over denominator square root of 83 end fraction
  • fraction numerator 10 over denominator square root of 83 end fraction
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19.

The lines p(p2+ 1) x – y + q = 0 and (p2+ 1)2x + (p2+ 1) y + 2q = 0 are
perpendicular to a common line for

  • no value of p

  • exactly one value of p

  • exactly two values of p

  • exactly two values of p

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20.

Let the line fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y minus 1 over denominator negative 5 end fraction space equals space fraction numerator straight z plus 2 over denominator 2 end fraction lie in the plane x + 3y – αz + β = 0. Then (α, β) equals

  • (6, – 17)

  • (–6, 7)

  • (5, –15)

  • (5, –15)

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