Home
Class 12
MATHS
Show that the vector area of the triangl...

Show that the vector area of the triangle whosse vertices have position vector `veca,vecb,vecc` is `1/2(vecaxxvecb+vecbxxvecc+veccxxveca)`.

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos

  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

Show that the vector area of the triangle whose vertices have position vectors vec(a),vec(b),vec(c ) , is 1/2(vec(a)xxvec(b)+vec(b)xxvec(c )+vec(c )xxvec(a)) .

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

For the non-zero vectors veca, vecb and vecc, veca.(vecbxxvecc) = 0 if

Find the area of triangle whose vertices are (1,2), (3,4),(1/2,1/4).

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

Three vectors veca, vecb and vecc satisfy the condition veca + vecb + vecc = 0 . Find the value of veca.vecb + vecb.vecc + vecc.veca if |veca| = 1, |vecb|= 4, |vecc|= 2 .

If veca , vecb and vecc are non-zero vectors, then vecaxxvecb = vecaxxvecc

If veca,vecb,vecc are unit vectors such that veca+vecb+vecc = vec0 , find the value of veca.vecb+vecb.vecc+vecc.veca .

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If the sum of two unit vectors is a unit vector, show that the magnitu...

    Text Solution

    |

  2. Find the foot of the perpendicular drawn from the point (5,7,3) to the...

    Text Solution

    |

  3. Show that the vector area of the triangle whosse vertices have positio...

    Text Solution

    |

  4. passing through the point (-1,3,2) perpendicular to the planes x+2y+...

    Text Solution

    |

  5. If y=x^(sinx)+(sinx)^(cosx), then find (dy)/(dx).

    Text Solution

    |

  6. Show that sin^(P) theta cos^(q) theta attains a maximum value, when th...

    Text Solution

    |

  7. Show that the sum of the intercepts on the coordinate axes of any tang...

    Text Solution

    |

  8. Prove by vector method that the mid-point of the hypotentise of a righ...

    Text Solution

    |

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

    Text Solution

    |

  10. Let f be defined by f(x)=4x + 3 for all x""inR. Show that it is biject...

    Text Solution

    |

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

    Text Solution

    |

  12. Prove that int0^(pi/2)lnSinxdx=-pi/2ln2

    Text Solution

    |

  13. Evaluate intfrac[dx][cosx(1+2sinx)]

    Text Solution

    |

  14. Solve the following differential equations (x+tany)dy= sin 2y ""dx

    Text Solution

    |

  15. Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),(2ab,b^2,a^2)) in the form of ...

    Text Solution

    |

  16. If A=[{:(2,1),(-1,3):}],B=[{:(2,3),(1,1):}]andC=[{:(1,0,2),(-2,3,0):}]...

    Text Solution

    |

  17. If f(x)=int0^x e^(2t).sin3tdtthen what is f^1(x)?

    Text Solution

    |

  18. What does the solution set of the inequation 2x+ygt5 represents?

    Text Solution

    |

  19. What is the value of tan(tan^-1""1/2+tan^-1""1/3).

    Text Solution

    |

  20. What is the general solution of tan^-1sqrt(dy/dx)=x?

    Text Solution

    |