Home
Class 12
MATHS
If bar(a),bar(b),bar(c) are any three ve...

If `bar(a),bar(b),bar(c)` are any three vectors, prove that (1) `[bar(a)+bar(b)" "bar(a)+bar(c)" "bar(b)]=[bar(a)" "bar(c)" "bar(b)]` (2) `[bar(a)-bar(b)" "bar(b)-bar(c)" "bar(c)-bar(a)]=0`.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple choice question|10 Videos

  • VECTORS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Theory Questions|4 Videos

  • TRIGONOMETRIC FUNCTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Multiple Choice Questions|12 Videos

Similar Questions

Explore conceptually related problems

If bar(a),bar(b)andbar(c) are any three vectors, prove that (1) [bar(a)+bar(b) bar(b)+bar(c) bar(c)+bar(a)]=2[bar(a)bar(b)bar(c)] (2) [bar(a) bar(b)+bar(c) bar(a)+bar(b)+bar(c)]=0

if bar(a),bar(b),bar(c) are any three vectors then prove that [bar(a),bar(b)+bar(c),bar(a)+bar(b)+bar(c)]=0

[bar(a)" "bar(b)+bar(c)" "bar(a)+bar(b)+bar(c)]=0

If bar(a)+bar(b)+bar(c), then

If [bar(a)+2bar(b)2bar(b)+bar(c)5bar(c)+bar(a)]=k[bar(a)bar(b)bar(c)]

If bar(a),bar(b),bar(c) are three non zero vectors,then bar(a).bar(b)=bar(a).bar(c)rArr

If bar(a),bar(b) and bar(c) are mutually perpendicular vectors then [bar(a)bar(b)bar(c)]=

bar(a) , bar(b) and bar(c) are three vectors such that bar(a) + bar(b) + bar(c) = bar(0) and |bar(a)| =2, |bar(b)| =3, |bar(c)| =5 ,then bar(a) . bar(b) + bar(b) . bar(c) + bar(c) . bar(a) equals

If bar(a),bar(b),bar(c) are non-coplanar vectors such that then bar(b)xxbar(c)=bar(a),bar(c)xxbar(a)=bar(b) and bar(a)xxbar(b)=bar(c), then |bar(a)+bar(b)+bar(c)|=

If bar(a),bar(b),bar(c) are coplanar then the value of |[bar(a),bar(b),bar(c)],[bar(a)*bar(a),bar(a)*bar(b),bar(a)*bar(c)],[bar(b).bar(a),bar(b)*bar(b),bar(b)*bar(c)]|=

NAVNEET PUBLICATION - MAHARASHTRA BOARD-VECTORS-Examples for Practics
  1. Express bar(p) as a linear combination of bar(a),bar(b)andbar(c), wher...

    Text Solution

    |

  2. Express the vector bar(a)=9hat(i)+hat(j)+2hat(k) as a linear combinati...

    Text Solution

    |

  3. If bar(a),bar(b),bar(c) are non-zero, non -coplanar vectors, then show...

    Text Solution

    |

  4. If bar(a)+lamdabar(b)+3bar(c),-2bar(a)+3bar(b)-4bar(c),bar(a)-3bar(b)+...

    Text Solution

    |

  5. D, E, F are the midpoints of the sides BC, CA and AB respectively of t...

    Text Solution

    |

  6. Show that if bar(AB)=bar(DC), then the figure ABCD is a parallelogram.

    Text Solution

    |

  7. If G is the centroid of triangleABC and O is any point in the plane of...

    Text Solution

    |

  8. Find [bar(a)bar(b)bar(c)] where : (1) bar(a)=2hat(i)+hat(j)-hat(k),b...

    Text Solution

    |

  9. If bar(a)=hat(i)+hat(j)+hat(k),bar(b)=2hat(i)+qhat(j)+hat(k),hat(c)=ha...

    Text Solution

    |

  10. Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2...

    Text Solution

    |

  11. Find the volume of the parallelopiped whose coterminus edges are : (...

    Text Solution

    |

  12. Find lamda, if the vectors bar(a)=hat(i)+hat(j)+hat(k),bar(b)=hat(i)-h...

    Text Solution

    |

  13. If bar(a),bar(b),bar(c) are any three vectors, prove that (1) [bar(a)...

    Text Solution

    |

  14. Find the volume of the parallelopiped with segments AB, AC and AD as c...

    Text Solution

    |

  15. Find the volume of the tetrahedron whose vertices are A(3,7,4),B(5,-2,...

    Text Solution

    |

  16. Find the volume tetrahedron whose coterminus edges are 7hat(i)+hat(k),...

    Text Solution

    |

  17. Show that the following sets of points are coplanar : (1) (3,9,4),(0...

    Text Solution

    |

  18. Find the value of x, if the points A(3,2,1),B(4,x,5),C(4,2,2)andD(6,5,...

    Text Solution

    |

  19. If the origin and the points P(2,3,4), Q(1,2,3) and R(x,y,z) are copla...

    Text Solution

    |

  20. If bar(u)=bar(i)-2bar(j)+bar(k),bar(v)=3bar(i)+bar(k)andbar(w)=bar(j)-...

    Text Solution

    |