The equation of the plane containing the line 2x-5y +z = 3, x +y

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The line passing through  - 1, π2 and perpendicular to 

3 + sinθ + 2cosθ = 4r is : 

  • 2 = 3rcosθ - 2rsinθ

  • 5 = - 23rsinθ +  4rsinθ

  • 2 = 3rcosθ +  2rsinθ

  • 5 = 23rsinθ +  4rcosθ


2.

If m1 and m2 are the roots of the equation x2 + 3 + 2x + 3 - 1 = 0,then the area of the triangle formed by the linesy = m1x, y = m2x and y = c

  • 33 - 114c2

  • 33 + 114c2

  • 11 - 332c2

  • 332c2


3.

 ABC is formed by A(1, 8, 4), B (0, - 11, 4) and C(2, - 3,1). If D is the foot of the perpendicular from A to BC. Then the coordinates of D are

  • ( - 4, 5, 2)

  • (4, 5, - 2)

  • (4,  - 5, 2)

  • (4,  - 5, - 2)


4.

The distance of the point (1, −5, 9) from the plane x−y+z=5 measured along the line x=y=z is:

  • 3√10

  • 10√3

  • 10/√3

  • 20/3

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5.

If the line   lies in the plane lx +my -z = 9, then l2 +m2 is equal to 

  • 26

  • 18

  • 5

  • 2

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6.

Locus the image of the point (2,3) in the line (2x - 3y +4) + k (x-2y+3) = 0, k ε R is a 

  • straight line parallel to X - axis

  • a straight line parallel to Y- axis

  • circle of radius square root of 2

  • circle of radius square root of 2

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7.

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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8.

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


C.

x+3y +6z = 7

Let equation of plane containing the lines 2x- 5y +z = 3 and x+y+4z = 5 be
(2x-5y+z-3) + λ(x+y+4z-5) = 0
⇒ (2+λ)x + (λ-5)y + (4λ + 1)z -3 -5λ =0... (i)
This plane is parallel to the plane x +3y +6z = 1

therefore space fraction numerator 2 plus straight lambda over denominator 1 end fraction space equals space fraction numerator straight lambda minus 5 over denominator 3 end fraction space equals space fraction numerator 4 straight lambda plus 1 over denominator 6 end fraction
On taking first two equalities, we get
6λ -30 = 3 + 12λ
-6λ = 33
λ = - 11/2
So, the equation of required plane is

open parentheses 2 minus 11 over 2 close parentheses space straight x space plus open parentheses fraction numerator negative 11 over denominator 5 end fraction minus 5 close parentheses straight y space plus open parentheses fraction numerator negative 44 over denominator 2 end fraction plus 1 close parentheses straight z space minus 3 space plus space 5 straight x space 11 over 2 space equals space 0
rightwards double arrow negative 7 over 2 space straight x minus 21 over 2 straight y minus 42 over 2 straight z plus 49 over 2 space equals space 0
rightwards double arrow space straight x space plus space 3 straight y space plus 6 straight z minus 7 space equals space 0

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9.

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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10.

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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