Home
Class 12
MATHS
Prove that the following. |[(v+w)^2,u^2...

Prove that the following. `|[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w^2,(u+v)^2]|=2uvw(u+v+w)^3`

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION SET

    USHA PUBLICATION|Exercise MODEL QUESTION SET|692 Videos

  • PREVIOUS YEAR QUESTION 2016

    USHA PUBLICATION|Exercise PREVIOUS YEAR QUESTION |44 Videos

Similar Questions

Explore conceptually related problems

Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^2,1,x+omega]] =0

Evaluate the following determinants. [[1,omega,omega^2],[omega,omega^2,1],[omega^2,1,omega]]

IF omega and omega^2 are the complex cube roots of unity, write the value of the following determinant. |{:(cos^2x,-1,sin^2x),(-2,1,1),(omega,omega^2,1):}|

if omega be the cube root of unit then what is the value of |[1,omega ,omega^2],[omega, omega^2,1],[omega^2,1,omega ]| ?

Derive the relation (v^2=u^2+2as) by calculus method.

USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Solve the following differential equations (1-x^2)(dy)/(dx)+2xy= x s...

    Text Solution

    |

  2. solve:e^-x(d^2y)/dx^2=x

    Text Solution

    |

  3. Find the scalar and vector projections of the vector 2hati-3hatj-6hatk...

    Text Solution

    |

  4. In any triangle ABC, prove by vector method that frac[a][sinA]=frac[b]...

    Text Solution

    |

  5. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

    Text Solution

    |

  6. Find the image of the point (3,5,7) with respect to the plane 2x+y+z=6...

    Text Solution

    |

  7. A variable plane is at a constant distance p from the origin and meets...

    Text Solution

    |

  8. Give an example of a relation f such that f = f^(-1)

    Text Solution

    |

  9. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

    Text Solution

    |

  10. Solve the following LPP graphically Optimize Z=5x1+25x2 subject to -0....

    Text Solution

    |

  11. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

    Text Solution

    |

  12. Find the inverse of the matrix abs[[3,-2,3],[2,1,-1],[4,-3,2]]

    Text Solution

    |

  13. If A=abs[[1,2,0],[1,1,0],[-1,4,0]],B=abs[[1,2,3],[1,1,-1],[4,-3,2]] a...

    Text Solution

    |

  14. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

    Text Solution

    |

  15. Find the coordinates of the point on the curve x^2y - x + y = 0 wher...

    Text Solution

    |

  16. Evaluate intln(x^2+x+2)dx

    Text Solution

    |

  17. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

    Text Solution

    |

  18. Solve the differential equation. x(x+y)dy=(x^2+y^2)dx

    Text Solution

    |

  19. If veca,vecb,vecc are three mutually perpendicular vectors of equal ma...

    Text Solution

    |

  20. Prove that the lines frac[x+3][2]=frac[y+5][3]=frac[z-7][-3] and frac[...

    Text Solution

    |