Home
Class 12
MATHS
Prove that (vec a+vec b)* (vec a+ vec b)...

Prove that `(vec a+vec b)* (vec a+ vec b)=|vec a|^2 +|vec b|^2, if and only if `vec a,vec b` are perpendicular.

Promotional Banner

Topper's Solved these Questions

  • VECTORS

    PRADEEP PUBLICATION|Exercise EXERCISE|438 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Prove that [vec a -vec b, vec b - vec c, vec c- vec a] =0

Show that ( vec a- vec b)xx( vec a+ vec b)=2( vec axx vec b)dot

If (vec a+ vec b)*(vec a- vec b)=0 and |vec a|=5 , find |vec b| .

If |quad vec a+ vec b|=|quad vec a- vec b| , prove that vec a and vec b are perpendicular.

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

Find |vec a| and |vec b| lf (veca + vec b)*(vec a-vec b)=8 and |vec a |=8|vec b| .

If (vec a+ vec b)* (vec a- vec b)=0 , show that |quad vec a|=|quad vec b| .

Does |quad vec a|= |quad vec b| imply vec a= vec b ?

If vec a and vec b are two vectors such that |quad vec a + vec b|= |quad vec a| , then prove that 2 vec a+ vec b is perpendicular to the vector vec b .

If (vec a)^2 =(vec b)^2 , is it necessary that vec a= vec b ?

PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. The scalar product of the vectorhat i+hat j+ hatk with a unit vector a...

    Text Solution

    |

  2. If vec a, vec b ,vec c are mutually perpendicular vectors of equal ma...

    Text Solution

    |

  3. Prove that (vec a+vec b)* (vec a+ vec b)=|vec a|^2 +|vec b|^2, if and ...

    Text Solution

    |

  4. If θ is the angle between two vectors vec a and vec b, then vec a*vec ...

    Text Solution

    |

  5. Let vec a and vec b be two unit vectors and θ is the angle between the...

    Text Solution

    |

  6. If (hat i, hat j, hat k) are the usual three perpendicular unit vector...

    Text Solution

    |

  7. If theta is the angle between any two vectors vec(a) and vec(b), "then...

    Text Solution

    |

  8. If vec a is a non-zero vector, then (1/|vec a|) vec a is a..........

    Text Solution

    |

  9. If vec a, vecb are non-collinear vectors, then vec a, vecb and vec a +...

    Text Solution

    |

  10. The vector veca+vecb bisects the angle between the non collinear vecto...

    Text Solution

    |

  11. If vec r* vec a =0 = vec r* vec b ,where vec a and vec b are non-copla...

    Text Solution

    |

  12. If vec r* vec a =0 = vec r* vec b =0 and also vec r* vec c =0 for som...

    Text Solution

    |

  13. If vec a and vec b are any two vectors, then (vec a xx vec b)^2 +(vec ...

    Text Solution

    |

  14. If vec a is any non-zero vector, then (vec a*hat i)hat i + (vec a*hat ...

    Text Solution

    |

  15. If a is any vector, then (a xxhati)^(2)+(axx hatj)^(2)+(axxhatk)^(2)...

    Text Solution

    |

  16. If (atimesb)^(2)+(a*b)^(2)=144 and |a|=4, then find the value of |b|.

    Text Solution

    |

  17. If a non-zero vector vec a makes an angle α with positive direction o...

    Text Solution

    |

  18. The values of k, for which |k vec a| lt |vec a| and k vec a =1/2 vec a...

    Text Solution

    |

  19. The vectors vec a=3 hat i+2 hat j+2hat k and vec b=-hat i +2hat k are ...

    Text Solution

    |

  20. If vec a and vec b are any two vectors, then (vec a+ vec b)^2 +(vec a-...

    Text Solution

    |