If the angle between the line x = and the plane x + 2y + 3z = 4

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 Multiple Choice QuestionsMultiple Choice Questions

341.

The distance of the point (1,0,2) from the point of intersection of the line fraction numerator straight x minus 2 over denominator 3 end fraction space equals space fraction numerator straight y plus 1 over denominator 4 end fraction space equals space fraction numerator straight z minus 2 over denominator 12 end fraction and the plane x-y +z = 16 is

  • 2 square root of 14
  • 8

  • 3 square root of 21
  • 3 square root of 21
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342.

The equation of the plane containing the line 2x-5y +z = 3, x +y+4z = 5 and parallel to the plane x +3y +6z =1 is

  • 2x + 6y + 12z = 13

  • x+3y+6z = -7

  • x+3y +6z = 7

  • x+3y +6z = 7

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343.

Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

  • 3/2

  • 5/2

  • 7/2

  • 7/2

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344.

If the lines

fraction numerator straight x minus 2 over denominator 1 end fraction space equals space fraction numerator straight y minus 3 over denominator 1 end fraction space equals space fraction numerator straight z minus 4 over denominator negative straight k end fraction
and
fraction numerator straight x minus 1 over denominator straight k end fraction space equals space fraction numerator straight y minus 4 over denominator 2 end fraction space equals space fraction numerator straight z minus 5 over denominator 1 end fraction
are coplanar, then k can have

  • any value

  • exactly one value

  • exactly two values

  • exactly two values

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345.

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


A.

2/3

fraction numerator straight x minus 0 over denominator 1 end fraction space equals space 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 space... space left parenthesis 1 right parenthesis
x + 2y + 3z = 4 ....... (2)

Angle between the line and plane is
cos space left parenthesis 90 minus space straight theta right parenthesis space equals space fraction numerator straight a subscript 1 straight a subscript 2 space plus straight b subscript 1 straight b subscript 2 space plus space straight c subscript 1 straight c subscript 2 over denominator square root of straight a subscript 1 superscript 2 plus straight b subscript 1 superscript 2 plus straight c subscript 1 superscript 2 end root space square root of straight a subscript 2 superscript 2 plus straight b subscript 2 superscript 2 plus straight c subscript 2 superscript 2 end root end fraction
rightwards double arrow space sin space straight theta space equals space fraction numerator 1 space plus space 4 space plus space 3 straight lambda over denominator square root of 14 space straight x space square root of 5 space plus space straight lambda squared end root end fraction space equals space fraction numerator 5 space plus space 3 straight lambda over denominator square root of 14 space straight x space end root square root of 5 space plus space straight lambda squared end root end fraction space... space left parenthesis 3 right parenthesis

But given that angle between line and plane is

rightwards double arrow space sin space straight theta space equals space fraction numerator 3 over denominator square root of 14 end fraction
therefore space from space left parenthesis 3 right parenthesis
fraction numerator 3 over denominator square root of 14 end fraction space equals space fraction numerator space 5 space plus space 3 straight lambda over denominator square root of 14 space end root space straight x square root of space 5 space plus straight lambda squared end root end fraction
rightwards double arrow space 9 space left parenthesis 5 space plus space straight lambda squared right parenthesis space equals space 25 space plus space 9 straight lambda squared space plus space 30 space straight lambda
30 space straight lambda space equals space 20
straight lambda space equals space 2 divided by 3
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346.

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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347.

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°

118 Views

348.

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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349.

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
857 Views

350.

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
205 Views

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