Home
Class 12
MATHS
Let a ,b ,c be real numbers with a^2+...

Let `a ,b ,c` be real numbers with `a^2+b^2+c^2=1.` Show that the equation `|a x-b y-c b x-a y c x+a b x+a y-a x+b y-cc y+b c x+a c y+b-a x-b y+c|=0` represents a straight line.

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

Factorize: a x+b x+a y+b y , a x^2+b y^2+b x^2+a y^2 , a^2+b c+a b+a c , a x-a y+b x-b y

Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2+2b x y+c y^2) .

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Solve: a x+b y=c ,\ \ \ \ b x+a y=1+c

Solve: a x+b y=c ,\ \ \ \ b x+a y=1+c

If x = 6a + 8b + 9c, y = 2b - 3a - 6c and z = c - b + 3a, find : x - y +z

Show that |a b c a+2x b+2y c+2z x y z|=0

If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

Divide: x^4-y^4b y\ x^2-y^2 (ii) a c x^2+\ (b c+a d)x+b d\ b y\ (a x+b)

The equation (b-c)x+(c-a)y+(a-b)=0 and (b^3-c^3)x+(c^3-a^3)y+a^3-b^3=0 will represent the same line if

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Let vec ar=xr hat i+yr hat j+zr hat k ,r=1,2,3 be three mutually perp...

    Text Solution

    |

  2. The number of distinct real roots of |[sinx,cosx,cosx],[cosx,sinx,cosx...

    Text Solution

    |

  3. Let a ,b ,c be real numbers with a^2+b^2+c^2=1. Show that the eq...

    Text Solution

    |

  4. If lines p x+q y+r=0,q x+r y+p=0 and r x+p y+q=0 are concurrent, the...

    Text Solution

    |

  5. If plambda^4+qlambda^3+rlambda^2+slambda+t=|[lambda^2+3lambda, lambda-...

    Text Solution

    |

  6. Find the value of lambdaif2x^2+7x y+3y^2+8x+14 y+lambda=0 represent a ...

    Text Solution

    |

  7. If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b...

    Text Solution

    |

  8. If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(...

    Text Solution

    |

  9. If a^2+b^2+c^2=1, then prove that |[a^2 +(b^2+c^2)cosθ, ab(1−cosθ), ...

    Text Solution

    |

  10. For the equation |[1,x,x^2],[x^2, 1,x],[x,x^2, 1]|=0, There are exa...

    Text Solution

    |

  11. Let Deltar=|[r-1,n,6],[(r-1)^2,2n^2,4n-2],[(r-1)^3,3n^3,3n^2-3n]|. Sho...

    Text Solution

    |

  12. Let m be a positive integer and Deltar=|[2r-1,.^mCr,1],[m^2-1,2^m,m+1]...

    Text Solution

    |

  13. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

    Text Solution

    |

  14. Find the area of a triangle whose vertices are A(3,2),B(11 ,8) and C(8...

    Text Solution

    |

  15. If Dk=1nn2k n^2+n+1n^2+n2k-1n^2n^2+n+1a n dsum(k=1)^n Dk=56. then n eq...

    Text Solution

    |

  16. If a!=p ,b!=q ,c!=r and |[p, b, c ],[a, q, c ],[a ,b, r]|=0, then find...

    Text Solution

    |

  17. If x1,x2,x3 as well as y1, y2, y3 are in G.P. with same common rati...

    Text Solution

    |

  18. If the lines a1x+b1y+1=0,a2x+b2y+1=0 and a3x+b3y+1=0 are concurrent,...

    Text Solution

    |

  19. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

    Text Solution

    |

  20. Find the value of a for which the lines 2x+y-1=0, a x+3y-3=0, 3x+2...

    Text Solution

    |