Home
Class 12
MATHS
Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x...

Prove that `a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0` represents a straight line parallel to the y-axis.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Prove that the equation 8x^2+8xy+2y^2+26x+13y+15=0 represents a pair of parallel straight lines . Also find the perpendicular distance between them .

Number of straight lines represented by x^5+y^5 = 0 is ……

If the equation 2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0 represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal to

If the equation 3x^(2)+xy-y^(2)-3x+6y+k=0 represents a pair of straight lines, then the value of k, is

Locus of the image of the point (2, 3) in the line (2x-3y""+""4)""+""k""(x-2y""+""3)""=""0,""kepsiR , is a : (1) straight line parallel to x-axis. (2) straight line parallel to y-axis (3) circle of radius sqrt(2) (4) circle of radius sqrt(3)

The value of lambda for which the equation x^2-y^2 - x - lambda y - 2 = 0 represent a pair of straight line, are

The equation x^(3)+x^(2)y-xy^(2)-y^(3)=0 represents three straight lines passing through the origin such that

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mu .

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mu .

If the equation x^2+(lambda+mu)x y+lambdau y^2+x+muy=0 represents two parallel straight lines, then prove that lambda=mudot

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

    Text Solution

    |

  2. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

    Text Solution

    |

  3. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

    Text Solution

    |

  4. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

    Text Solution

    |

  5. The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...

    Text Solution

    |

  6. Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a ...

    Text Solution

    |

  7. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

    Text Solution

    |

  8. 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, th...

    Text Solution

    |

  9. Prove that |2alpha+beta+gamma+deltaalphabeta+gammadelta alpha+beta+g...

    Text Solution

    |

  10. Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]|=0.

    Text Solution

    |

  11. The value of the determinant |{:(1,,1,,1),(.^(m)C(1),,.^(m+1)C(1),...

    Text Solution

    |

  12. Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a...

    Text Solution

    |

  13. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

    Text Solution

    |

  14. Consider the set A of all determinants of order 3 with entries 0 or 1 ...

    Text Solution

    |

  15. Solve: |[x^2-1, x^2+2x+1, 2x^2+3x+1], [2x^2+x-1, 2x^2+5x-3, 2x^2+4x-3...

    Text Solution

    |

  16. If |[x,3, 6],[ 3, 6,x],[6,x,3]|=|[2,x,7],[x,7, 2],[ 7, 2,x]|=|[4, 5,x]...

    Text Solution

    |

  17. If A1B1C1 , A2B2C2 and A3B3C3 are three digit numbers, each of which ...

    Text Solution

    |

  18. If f^(prime)(x)=|[mx, mx-p, m x+p], [n, n+p, n-p], [mx+2n, m x+2n+p, m...

    Text Solution

    |

  19. If sum(n=1)^nalphan=a n^2+b n ,w h e r ea ,b are constants and alp...

    Text Solution

    |

  20. The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

    Text Solution

    |