Home
Class 12
MATHS
Let a ,b , c be the real numbers. The fo...

Let `a ,b , c` be the real numbers. The following system of equations in `x ,y ,a n dz` `(x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1,(x^2)/(a^2)-(y^2)/(b^2)+(z^2)/(c^2)=1,-(x^2)/(a^2)+(y^2)/(b^2)+(z^2)/(c^2)=1` has a. no solution b. unique solution c. infinitely many solutions d. finitely many solutions

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If x+y+z=x y z prove that (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)=(2x)/(1-x^2)(2y)/(1-y^2)(2z)/(1-z^2)dot

If x=asec thetacosphi,y=bsec thetasin phi and z=ctantheta, show that, (x^2)/(a^2)+(y^2)/(b^2)-(z^2)/(c^2)=1

Express (x^(2)+a^(2))(y^(2)+b^(2))(z^(2)+c^(2)) as the sum of two squares.

If x y=2(x+y),xlt=y and x ,y in N , then the number of solutions of the equation are a. two b. three c. no solution d. infinitely many solutions

Show that the following system of equations has no solution : x+2y+3z=1,2x+3y+5z=1,3x+4y+7z=1

If x=a sec theta cosphi, y = b sec theta sin phi and z=c tan theta , then prove that (x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=1.

If x/a = y/b = z/c , then show that (x^(2)-yz)/(a^(2)-bc) = (y^(2)-zx)/(b^(2) - ca) = (z^(2)-xy)/(c^(2)-ab)

Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) , ((c-x)^2,(c-y)^2, (c-z)^2)) = 2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

Represent the following equations in matrix form: a_(1)x+b_(1)y+c_(1)z=k_(1) a_(2)x+b_(2)y+c_(2)z=k_(2) a_(3)x+b_(3)y+c_(3)z=k_(3)

Solve the system of the equations: a x+b y+c z=d , a^2x+b^2y+c^2z=d^2 , a^3x+b^3y+c^3z=d^3 .

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the va...

    Text Solution

    |

  2. If the determinant |[b-c,c-a, a-b],[b^(prime)-c ', c^(prime)-a ', a^(p...

    Text Solution

    |

  3. Let a ,b , c be the real numbers. The following system of equations in...

    Text Solution

    |

  4. By using properties of determinats. Prove that- |(sintheta,costheta,...

    Text Solution

    |

  5. Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...

    Text Solution

    |

  6. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |

  7. Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B...

    Text Solution

    |

  8. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

    Text Solution

    |

  9. 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...

    Text Solution

    |

  10. If (x)=|(alpha+x,theta+x,lambda+x),(beta+x,varphi+x,mu+x),(gamma+x,psi...

    Text Solution

    |

  11. If alpha,beta,gamma are different from 1 and are the roots of a x^3+b ...

    Text Solution

    |

  12. If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],...

    Text Solution

    |

  13. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

    Text Solution

    |

  14. If 2s=a+b+c and A=|[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[(s-c)^...

    Text Solution

    |

  15. Find the value of lambda for which |{:(2a1+b1 , 2a2+b2 , 2a3+b3),(2b1+...

    Text Solution

    |

  16. Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c...

    Text Solution

    |

  17. if a determinant of order 3xx 3 is formed by using the numbers 1 ...

    Text Solution

    |

  18. If z=|[-5, 3+4i,5-7i],[3-4i,6 ,8+7i],[5+7i,8-7i,9]|,t h e nz is (a) p...

    Text Solution

    |

  19. Consider the following linear equations: a x+b y+c z=0 b x+c y+a z=0 c...

    Text Solution

    |

  20. Let omega be the complex number cos(2pi/3)+isin(2pi/3) Then the number...

    Text Solution

    |