Home
Class 12
MATHS
Consider the following linear equations:...

Consider the following linear equations: `a x+b y+c z=0` `b x+c y+a z=0` `c x+a y+b z=0` Match the expression/statements in column I with expression/statements in Column II. Column I, Column II `a+b+c!=0`and `a^2+b^2+c^2=a b+b c+c a` , p. the equations represent planes meeting only at a single point `a+b+c=0a n da^2+b^2+c^2!=a b+b c+c a` , q. the equations represent the line `x=y=z` `a+b+c!=0a n da^2+b^2+c^2!=a b+b c+c a` , r. the equations represent identical planes `a+b+c!=0` and `a^2+b^2+c^2!=a b+b c+c a` , s. the equations represent the whole of the three dimensional space

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 the parabola y=(a-b)x^2+(b-c)x+(c-a) touches x- axis then the line ax+by+c=0

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.

Let f(x)=a x^2+b x+cdot Consider the following diagram. Then Fig c 0 a+b-c >0 a b c<0

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

If the foot of the perpendicular from the origin to plane is P(a ,b ,c) , the equation of the plane is a. x/a=y/b=z/c=3 b. a x+b y+c z=3 c. a x+b y+c z=a^(2)+b^2+c^2 d. a x+b y+c z=a+b+c

Match the statements/expressions given in Column I with the values given in Column II. Column I, Column II sum_(i=1)^ootan^(-1)(1/(2i^2))=1,t h e ntant= , Sides a , b , c for a triangle ABC are in A.P. and costheta_1=a/(b+c), costheta_2=b/(a+c), costheta_3=c/(a+b), then tan^(2)((theta_1)/2)+tan^2((theta_3)/2)= , 1 A line is perpendicular to x+2y+2z=0 and passes through (0,10). The perpendicular distance of this line from the origin is , (sqrt(5))/3

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

Consider the lines L_1:(x-1)/2=y/(-1)=(z+3)/1,L_2:(x-4)/1=(y+3)/1=(z+3)/2 and the planes P_1:7x+y+2z=3,P_2:3x+5y-6z=4. Let a x+b y+c z=d be the equation of the plane passing through the point match Column I with Column II. Column I, Column II a= , p. 13 b= , q. -3 c= , r. 1 d= , s. -2

Consider the equation az+b bar(z)+c=0" ""where" " "a,b,cin Z If |a|!=|b|, then z represents

If a system of three linear equations x+4a y+a=0,x+3b y+b=0, and x+2c y+c=0 is consistent, then prove that a ,b , c are in H.P.

CENGAGE PUBLICATION-DETERMINANTS-All Questions
  1. if a determinant of order 3xx 3 is formed by using the numbers 1 ...

    Text Solution

    |

  2. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. If omega is the complex cube root of unity then |[1,1+i+omega^2,omeg...

    Text Solution

    |

  6. Consider the determinant Delta=|[a1+b1x^2,a1x^2+b1,c1],[a2+b2x^2,a2x^2...

    Text Solution

    |

  7. If a x1^2+b y1^2+c z1^2=a x2 ^2+b y2 ^2+c z2 ^2=a x3 ^2+b y3 ^2+c z3 ^...

    Text Solution

    |

  8. If A , B ,a n dC are the angles of triangle, show that the system of...

    Text Solution

    |

  9. Let alpha,beta,gamma are the real roots of the equation x^3+a x^2+b x+...

    Text Solution

    |

  10. If a1, a2, a3,54,a6,a7, a8, a9 are in H.P., and D=|[a1,a2,a3],[5, 4,a6...

    Text Solution

    |

  11. If f(x) is a polynomial of degree <3, then, f(x)/((x−a)(x−b)(x−c))​is ...

    Text Solution

    |

  12. Prove that =|[a,c,c-a,a+c],[c,b,b-c,b+c],[a-b,b-c,0,a-c],[x,y,z,1+x+y]...

    Text Solution

    |

  13. Solve for x in R : |((x+a)(x-a),(x+b)(x-b),(x+c)(x-c)),((x-a)^3,(x-b)...

    Text Solution

    |

  14. Absolute value of sum of roots of the equation |[x+2,2x+3, 3x+4],[ 2x+...

    Text Solution

    |

  15. Let alpha1,alpha2 and beta1, beta2 be the roots of the equation ax^2+b...

    Text Solution

    |

  16. The product of all values of t , for which the system of equations (a-...

    Text Solution

    |

  17. "If " a(1) ,a(2), a(3)….." are in A.P, then find the value of the fol...

    Text Solution

    |

  18. Let omega=-1/2+i(sqrt(3))/2. Then the value of the determinant |(1,1,1...

    Text Solution

    |

  19. 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+...

    Text Solution

    |

  20. If g(x)=|[a^(-x),e^(x loge a),x^2],[a^(-3x),e^(3x loge a),x^4],[a^(-5x...

    Text Solution

    |