Home
Class 12
MATHS
Three vectors vec(a),vec(b) and vec( c )...

Three vectors `vec(a),vec(b)` and `vec( c )` satisfy the condition
`vec(a)+vec(b)+vec( c )=vec(0)`. Evaluate the quantity `mu=vec(a).vec(b)+vec(b).vec( c )+vec( c ).vec(a)`, if `|vec(a)|=1,|vec(b)|=4` and `|vec( c )|=2`.

Text Solution

Verified by Experts

The correct Answer is:
`2mu=-21` i.e., `mu=(-21)/(2)`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|17 Videos

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Objective type Questions)|23 Videos

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise MISCELLANEOUS EXERCISE - 10|19 Videos

  • THREE DIMENSIONAL GEOMETRY

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER -11|16 Videos

Similar Questions

Explore conceptually related problems

For three vectors vec(a),vec(b) and vec( c ),vec(a)+vec(b)+vec( c )=vec(0)|vec(a)|=3,|vec(b)|=4,|vec( c )|=5 , then evaluate 2(vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a)) .

Prove that [vec(a)+vec(b), vec(b)+vec( c ), vec( c )+vec(a)]=2[vec(a),vec(b),vec( c )] .

Three vector vec(A) , vec(B) , vec(C ) satisfy the relation vec(A)*vec(B)=0 and vec(A).vec(C )=0 . The vector vec(A) is parallel to

Show that the vectors vec(a),vec(b) and vec( c ) coplanar if vec(a)+vec(b),vec(b)+vec( c ) and vec( c )+vec(a) are coplanar.

Let vec(a),vec(b) and vec( c ) be three unit vectors such that vec(a),+vec(b)+vec( c )=vec(0) . If lambda=vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a) and vec(d)=vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xx vec(a) then the ordered pair (lambda, vec(d)) is equal to :

If |vec(a)|=2|vec(b)|=5 and |vec(a)xx vec(b)|=8 then find vec(a).vec(b) .

If |vec(a)|=2,|vec(b)|=5 and vec(a).vec(b)=10 then find |vec(a)-vec(b)| .

For vectors vec(a),vec(b) and vec( c ),vec(a).vec(b)=vec(a).vec( c ) and vec(a)xx vec(b)=vec(a)xx vec( c ),vec(a) ne vec(0) then show that vec(b)=vec( c ) .

Prove that [vec(a),vec(b),vec( c )+vec(d)]=[vec(a),vec(b),vec( c )]+[vec(a),vec(b),vec(d)] .

KUMAR PRAKASHAN-VECTOR ALGEBRA -Textbook Illustrations for Practive Work
  1. Find |vec(a)-vec(b)|, if two vectors vec(a) and vec(b) are such that |...

    Text Solution

    |

  2. If vec(a)is a unit vector and (vec(x)-vec(a)).(vec(x)+vec(a))=8 then f...

    Text Solution

    |

  3. For any two vectors vecaandvecb , we always have |veca*vecb|le|veca||v...

    Text Solution

    |

  4. For any two vectors vec(a) and vec(b), we always have |vec(a)+vec(b)|l...

    Text Solution

    |

  5. Show that the points A(-2hati+3hatj+5hatk),B(hati+2hatj+3hatk)andC(7ha...

    Text Solution

    |

  6. Find |vecaxxvecb|, if veca=2hati+hatj+3hatk and vecb=3hati+5hatj-2hatk

    Text Solution

    |

  7. Find a unit vector perpendicualr to each of the vectors (vec(a)+vec(b)...

    Text Solution

    |

  8. Find the area of atriangle having the points A(1,1,1), B (1,2,3) and C...

    Text Solution

    |

  9. Find the area of a parallelogram whose adjacent sides are given by the...

    Text Solution

    |

  10. If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+...

    Text Solution

    |

  11. Show that the vectors vec(a)=hati-2hatj+3hatk,vec(b)=-2hati+3hatj-4hat...

    Text Solution

    |

  12. If the vectors vec(a)=hati+3hatj+hatk,vec(b)=2hati-hatj-hatk and vec( ...

    Text Solution

    |

  13. If 4hati+5hatj+hatk,-(hatj+hatk),3hati+9hatj+4hatk and 4(-hati+hatj+ha...

    Text Solution

    |

  14. Prove that [vec(a)+vec(b), vec(b)+vec( c ), vec( c )+vec(a)]=2[vec(a)...

    Text Solution

    |

  15. Prove that [vec(a),vec(b),vec( c )+vec(d)]=[vec(a),vec(b),vec( c )]+[v...

    Text Solution

    |

  16. Write all the unit vectors in XY-plane.

    Text Solution

    |

  17. If hati+hatj+hatk,2hati+5hatj,3hati+2hatj-3hatk and hati-6hatj-hatk ar...

    Text Solution

    |

  18. Let vec(a),vec(b) and vec( c ) be three vectors such that |vec(a)|=3,|...

    Text Solution

    |

  19. Three vectors vec(a),vec(b) and vec( c ) satisfy the condition vec(a...

    Text Solution

    |

  20. If with reference to the right handed system of mutually perpendicular...

    Text Solution

    |