Home
Class 12
MATHS
Prove the following: |[ax-by-cz,ay+bx,...

Prove the following:
`|[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],[cx+az,ay+bz,cz-ax-by]|`
=`(a^2+b^2+c^2)(ax+by+cz)(x^2+y^2+z^2)`

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 5

    MODERN PUBLICATION|Exercise PROBLEM|41 Videos

  • TEST PAPER 7

    MODERN PUBLICATION|Exercise EXERCISE|39 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following: intx^2e^(ax)dx

If ax+by +cz=X,cx+by +az=Y,bx+ay+cz=Z show that (a^2+b^2+c^2-ab-bc-ca)(x^2+y^2+z^2-xy-yz-zx) =X^2+Y^2+Z^2-YZ-ZX-XY

Find derivatives of the following functions. sqrt(ax^2 + bx + c)

Prove that the circles given by x^2+y^2+2ax+2by+c=0 , and x^2+y^2+2bx+2ay+c=0 , touch each other, if (a + b)^2 = 2c.

int_0^ax^3(a^2-x^2)^(5/2)dx

Find derivatives of the following functions. cosec (ax + b)^2

Find the centre and radius of the following circles : a(x^2 + y^2) - bx - cy = 0

If y = ax sin x show that x^2y_2 - 2xy_1 + (x^2 + 2)y = 0

Prove that the lines x = ay + b, z = cy + d and x = a'y + b' , z= c'y + d' are perpendicular, if a a' + c c' + 1=0

Prove that the lines x=az+b,y=cz+d and x=a_1z + b_1,y=c_1z+d_1 are perpendicular if aa_1+"cc"_1+1=0.

MODERN PUBLICATION-TEST PAPER 6-EXERCISE
  1. Evaluate:int (sin x-xcosx)/(x(x+sinx)) dx.

    Text Solution

    |

  2. Integrate : int sin^(-1)xdx.

    Text Solution

    |

  3. Find the particular solution of d^2 y/dx^2 =2x,given that x=0,y=2 and ...

    Text Solution

    |

  4. Solve :-(x^2+y^2)dx-2xy dy=0

    Text Solution

    |

  5. If with reference to the eight handed system of mutually perpendicular...

    Text Solution

    |

  6. If vec a =(2,3,6), vec b=(2,-2,1), vec c=(-1,0,2), find the direction ...

    Text Solution

    |

  7. Find the equation of the plane passing through (1, 3,4), (2, 1.-1) an...

    Text Solution

    |

  8. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

    Text Solution

    |

  9. Find the distance of the point (-1,-5,-10) from the point of intersect...

    Text Solution

    |

  10. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

    Text Solution

    |

  11. Let A=R-{3/5} Br f:ArarrA defined as f(x)=(3x+2)/(5x-3). Br show that ...

    Text Solution

    |

  12. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

    Text Solution

    |

  13. Find the inverse of the following matrices using elementary transforma...

    Text Solution

    |

  14. Show that the homogenous system of equations x-2y+z = 0 x+y-z = 0 ...

    Text Solution

    |

  15. (i) if x=sint, y= sinpt, then show that (1-x^2) d^2 y/dx^2 - x dy/dx +...

    Text Solution

    |

  16. A cylindrical open water tank with a circular base is to be made out o...

    Text Solution

    |

  17. Evaluate int (x^2 dx)/((x^2 +1)(x^2 +4))

    Text Solution

    |

  18. Determine the area of the region bounded by y^2=4ax by the double ordi...

    Text Solution

    |

  19. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

    Text Solution

    |

  20. Show that the lines (x-4)/1=(y+3)/-4=(z+1)/7 and (x-1)/2=(y+1)/-3=(z+1...

    Text Solution

    |