Home
Class 12
MATHS
If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^...

If `|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0` and x, y, z are all distince, then xysz equals

Text Solution

Verified by Experts

The correct Answer is:
1
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DETERMINANT

    FIITJEE|Exercise MATCH THE COLUMNS|5 Videos
  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • ELLIPSE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

Similar Questions

Explore conceptually related problems

If |(x, x^2, x^3 +1), (y, y^2, y^3+1), (z, z^2, z^3+1)| = 0 and x ,y and z are not equal to any other, prove that, xyz = -1

If |[x^3+1, x^2, x] , [y^3+1, y^2, y] , [z^3+1, z^2, z]|=0 and x, y, z are all different then prove that xyz=-1

Knowledge Check

  • If |(x,x^2,1+x^3),(y,y^2,1+y^2),(z,z^2,1+z^3):|=0 and x,y,z are all distinct, then xyz is equal to

    A
    -1
    B
    1
    C
    0
    D
    3
  • If |(x,x^2,1+x^3),(y,y^2,1+y^2),(z,z^2,1+z^3):|=0 and x,y,z are all distinct, then xyz is equal to

    A
    -1
    B
    1
    C
    0
    D
    3
  • If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 then relation of x,y and z is

    A
    `ane1`
    B
    `a=1`
    C
    `a=0`
    D
    `a=-1`
  • Similar Questions

    Explore conceptually related problems

    If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, then the value of x y z is a.1 b. 2 c. -1 d. 2

    Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3)):}|=|{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x)

    If x,y,z are all distinct and |(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^2,1+z^3)|=0 then the value of xyz is

    If |(x^(n),x^(n+2),x^(n+3)),(y^(n),y^(n+2),y^(n+3)),(z^(n),z^(n+2),z^(n+3))| = (x -y) (y -z) (z -x) ((1)/(x) + (1)/(y) + (1)/(z)) , then n equals

    If x=1/3y and y=1/2 z .then x: y : z , is equal to :