Home
Class 12
MATHS
Show that [veca+vecbvecb+veccvecc+veca] ...

Show that `[veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]`

Promotional Banner

Topper's Solved these Questions

  • PREVIOUS YEAR QUESTION 2017

    USHA PUBLICATION|Exercise PREVIOUS YEAR QUESTION |51 Videos

  • PREVIOUS YEAR QUESTION 2019

    USHA PUBLICATION|Exercise PREVIOUS YEAR QUESTION |46 Videos

Similar Questions

Explore conceptually related problems

Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

Show that veca, vecb and vec c are coplanar if veca+vecb,vecb+vecc and vecc+veca are coplanar.

For any three vectors veca,vecb,vecc show that [(veca-vecb) (vecc-veca) (vecb-vecc)] = 0

Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) . Interpret this result geometrically.

For veca = hati+hatj, vecb = -hati+2hatk, vecc = hatj+hatk , obtain vecaxx(vecbxxvecc) and also verify the formula vecaxx(vecbxxvecc) = (veca.vecc)vecb-(veca.vecb)vecc .

If veca, vecb, vecc are mutually perpendicular vectors of equal magnitude, show that veca+vecb+vecc is equally inclined to veca.vecb.vecc .

If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-vecb)^2 . [(veca+vecb)^2 means (veca+vecb).(veca+vecb) , so does (veca-vecb)^2 .]

If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that veca = vec0 or vecb = vecc or veca is perpendicular to vecb.vecc .

|veca| = |vecb| = veca = vecb .

Prove that the four points with position vectors 2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc and veca-6vecb+6vecc are coplanar.

USHA PUBLICATION-PREVIOUS YEAR QUESTION 2018-PREVIOUS YEAR QUESTION
  1. From the differential equation whose general solution is y=asint+be^t.

    Text Solution

    |

  2. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

    Text Solution

    |

  3. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

    Text Solution

    |

  4. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

    Text Solution

    |

  5. If the sum of two unit vectors is a unit vector, show that the magnitu...

    Text Solution

    |

  6. Prove that the measure of the angle between two main diagonals of a cu...

    Text Solution

    |

  7. If the position vectors of two points A and B are 3hati + hatk and 2ha...

    Text Solution

    |

  8. If A and B are invertible matrices of the same order, then prove that ...

    Text Solution

    |

  9. In a triangle ABC "if" m/A =90^@, "prove that "tan"^(-1) b/(a+b) +"ta...

    Text Solution

    |

  10. Solve the following LPP graphically: Maximize Z=3x1+2x2, x1le2, x1+x2l...

    Text Solution

    |

  11. Solve the following system of equations by the matrix inversion method...

    Text Solution

    |

  12. Two cards are drawn successively with replacement from a well-shuffled...

    Text Solution

    |

  13. By elementary operations, find A^(-1) for the following: A=[[1,1,0],[1...

    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 intfrac[2cosx+7][4-sinx]dx

    Text Solution

    |

  17. Find the solution of the following differential equations: (4x+6y+5)dx...

    Text Solution

    |

  18. Find the area enclosed bt the two paraboles y^2=4 ax and x^2=4ay.

    Text Solution

    |

  19. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

    Text Solution

    |

  20. Find the shortest distance between the lines (x-3)/3=(y-8)/(-1)=(z-3)/...

    Text Solution

    |