Home
Class 12
MATHS
If vec(a),vec(b),vec( c ) are mutually p...

If `vec(a),vec(b),vec( c )` are mutually perpendicular vectors of equal magnitudes, show that the vector `vec(a)+vec(b)+vec( c )` is equally inclined to `vec(a),vec(b)` and `vec( c )`.

Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practive Work|36 Videos

  • VECTOR ALGEBRA

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

  • VECTOR ALGEBRA

    KUMAR PRAKASHAN|Exercise EXERCISE-10.5|8 Videos

  • THREE DIMENSIONAL GEOMETRY

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER -11|16 Videos

Similar Questions

Explore conceptually related problems

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.

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

If |vec(a)xx vec(b)|=vec(a).vec(b) then find the angle between vec(a) and vec(b) .

The vectors vec(a) and vec(b) are not perpendicular. The vectors vec( c ) and vec(d) are such that vec(b)xx vec( c )=vec(b)xx vec(d) and vec(a).vec(d)=0 then vec(d) = ……………

Let vec(a),vec(b) and vec( c ) are three unit vectors such that vec(a)xx(vec(b)xx vec( c ))=(sqrt(3))/(2)(vec(b)+vec( c )) . If the vectors vec(b) and vec( c ) are not parallel then the angle between vec(a) and vec(b) is ……….

If vec(a)=hati+hatj+hatk,vec( c )=hatj-hatk are given vectors, then find a vector vec(b) satisfying the equations vec(a)xx vec(b)=vec( c ) and vec(a).vec(b)=3 .

If vec(a)+vec(b)+vec( c )=0 and |vec(a)|=6,|vec(b)|=5,|vec( c )|=7 then find the angle between the vectors vec(b) and vec( c ) .

Let vec(a),vec(b) and vec( c ) be unit vectors such that vec(a).vec(b)=vec(a).vec( c )=0 and the angle between vec(b) and vec( c ) is (pi)/(6) . Prove that vec(a)=+-2(vec(b)xx vec( c )) .

Find |vec(a)-vec(b)| , if two vectors vec(a) and vec(b) are such that |vec(a)|=2,|vec(b)|=3 and vec(a).vec(b)=4 .

KUMAR PRAKASHAN-VECTOR ALGEBRA -MISCELLANEOUS EXERCISE - 10
  1. Write down a unit vector in XY-plane, making an angle of 30^(@) with t...

    Text Solution

    |

  2. Find the scalar components and magnitude of the vector joining the poi...

    Text Solution

    |

  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30^...

    Text Solution

    |

  4. If veca=vecb+vecc , then is it true that |veca|=|vecb|+|vecc|? Justify...

    Text Solution

    |

  5. Find the value of x for which x(hati+hatj+hatk) is a unit vector.

    Text Solution

    |

  6. Find a vector of magnitude 5 units and parallel to the resultant of th...

    Text Solution

    |

  7. If veca=hati+hatj+hatk,vecb=2hatj-hatj+3hatkandvecc=hati-2hatj+hatk, ...

    Text Solution

    |

  8. Show that the points A(1,-2,-8),B(5,0,-2)andC(11,3,7) are collinear , ...

    Text Solution

    |

  9. Find the position vector of a point R which divides the line joining t...

    Text Solution

    |

  10. The two adjacent sides of a parallelogram are 2hati-4hatj+5hatk and ha...

    Text Solution

    |

  11. Show that the direction cosines of a vector equally inclined to the ax...

    Text Solution

    |

  12. Let vec(a)=hati+4hatj+2hatk,vec(b)=3hati-2hatj+7hatk and vec( c )=2hat...

    Text Solution

    |

  13. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

    Text Solution

    |

  14. If vec(a),vec(b),vec( c ) are mutually perpendicular vectors of equal ...

    Text Solution

    |

  15. prove that (vec(a)+vec(b)).(vec(a)+vec(b))=|vec(a)|^(2)+|vec(b)|^(2), ...

    Text Solution

    |

  16. If theta is angle between two vectors vec(a) and vec(b) then vec(a).ve...

    Text Solution

    |

  17. Let vec(a) and vec(b) be two unit vectors and theta is the angle betwe...

    Text Solution

    |

  18. The value of hati.(hatj xx hatk)+hatj.(hati xx hatk)+hatk.(hati xx hat...

    Text Solution

    |

  19. If theta is the angle between any two vectors vecaandvecb, then |veca*...

    Text Solution

    |