Home
Class 12
MATHS
If vec a and vec b be perpendicular vect...

If `vec a` and `vec b` be perpendicular vectors, then prove that `(vec a + vec b)^(2) = (vec a - vec b)^(2)`.

Promotional Banner

Topper's Solved these Questions

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise EXERCISE|40 Videos

Similar Questions

Explore conceptually related problems

Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2) .

If vec a , vec b , vec c are mutually perpendicular vectors of equal magnitude show that vec a+vec b+vec c is equally inclined to vec a , vec b , vec c .

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(b) + vec(c) = vec(0) , then prove that vec(a) xx vec(b) = vec(b) xx vec(c) = vec(c) xx vec(a) .

Prove that |vec(a)-vec(b)|ge|vec(a)|-|vec(b)| .

If vec a , vec b , vec c are unit vectors and vec a + vec b + vec c = 0 then the evaluate vec a. vec b + vec b.vec c + vec c.vec a .

MODERN PUBLICATION-VECTOR-EXERCISE
  1. Determine the area of parallelogram whose adjacent sides are the vecto...

    Text Solution

    |

  2. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

    Text Solution

    |

  3. Prove that (vec a × vec b).(vec c × vec d) = [[vec a.vec c,vec a.vec d...

    Text Solution

    |

  4. Find a unit vector in direction of vec a-vec b, when vec a = 4 hat i +...

    Text Solution

    |

  5. If vec a and vec b be perpendicular vectors, then prove that (vec a + ...

    Text Solution

    |

  6. Find the value of lambda so that the three vectors are co-planar. (2,-...

    Text Solution

    |

  7. Determine k such that a vector vec(r) is at right angles to each of th...

    Text Solution

    |

  8. Find the scalar and vector projection of veca on vecb. veca = hati+hat...

    Text Solution

    |

  9. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

    Text Solution

    |

  10. Prove that : |veca + vecb|le|veca|+|vecb|.

    Text Solution

    |

  11. Show that vec a × (vec b+vec c) + vec b × (vec c+vec a) + vec c × (vec...

    Text Solution

    |

  12. If vec(a) and vec(b) are unit vectors, then what is the angle between ...

    Text Solution

    |

  13. Prove by vector method that the diagonals of a parallelogram bisect ea...

    Text Solution

    |

  14. Prove by vector method that in a parallelogram, the line joining a ve...

    Text Solution

    |

  15. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

    Text Solution

    |

  16. Prove the following by vector method. Median to the base of an isoscel...

    Text Solution

    |

  17. Prove the following by vector method. The diagonals of a rhombus are a...

    Text Solution

    |

  18. Prove the following by vector method. An angle inscribed in a semi-cir...

    Text Solution

    |

  19. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

    Text Solution

    |

  20. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

    Text Solution

    |