The distance of the point (1, −5, 9) from the plane x−y+z=5

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 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)


Advertisement

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


B.

10√3

the equation of the line passing through the point (1,5-9 and parallel to x =y=z is


fraction numerator straight x minus 1 over denominator 1 end fraction space equals space fraction numerator straight y plus 5 over denominator 1 end fraction space equals space fraction numerator straight z minus 9 over denominator 1 end fraction space equals space straight lambda
Thus, any point on this line is of the form
(λ +1, λ-5 ,λ+9) 
Now, if P (λ +1, λ-5, λ+9) is the point of intersection of line and plane, then
 (λ+1) - (λ-5) +λ+9 = 5
λ +15 = 5
λ = -10
therefore coordinates of point P are (-9, -15,-1)
Hence, required distance
=equals square root of left parenthesis 1 plus 9 right parenthesis squared plus left parenthesis negative 5 plus 15 right parenthesis squared plus left parenthesis 9 plus 1 right parenthesis squared end root
equals square root of 10 squared plus space 10 squared plus 10 squared end root space equals space 10 square root of 3

414 Views

Advertisement
Advertisement
5.

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

  • 26

  • 18

  • 5

  • 2

224 Views

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

654 Views

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
169 Views

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

455 Views

Advertisement
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

250 Views

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

157 Views

Advertisement