Home
Class 12
MATHS
If veca and vecb are two vectors and ang...

If `veca and vecb` are two vectors and angle between them is `theta` , then

A

`|atimesb|^(2)+(a*b)^(2)=|a|^(2)|b|^(2)`

B

`|atimesb|=(a*b), if theta=(pi)/(4)`

C

`atimesb=(a*b)hat(n)`, (where `hat(n)` is a normal unit vector), if `theta=(pi)/(4)`

D

`|atimesb|*(a+b)=0`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|12 Videos
  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos
  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|73 Videos
  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos
  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

If veca and vecb are two unit vectors and the angle between them is 60^(@) then ((1+veca.vecb))/((1-veca.vecb)) is

If veca and vecb are two unit vectors and theta is the angle between them, then the unit vector along the angular bisector of veca and vecb will be given by

If veca and vecb are unit vector and theta is the angle between then, then |(veca - vecb)/2| is:

Let veca and vecb be two unit vectors and alpha be the angle between them, then veca + vecb is a unit vector , if alpha =

vecA and vecB are two vectors and theta is the angle between them, if |vecA xx vecB|=sqrt(3)(vecA.vecB) the value of theta is:-

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: The value of sin(theta/2) is (A) 1/2 |veca-vecb| (B) 1/2|veca+vecb| (C) |veca-vecb| (D) |veca+vecb|

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca, |veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If vecc is a unit vector and equal to the sum of veca and vecb the magnitude of difference between veca and vecb is (A) 1 (B) sqrt(2) (C) sqrt(3) (D) 1/sqrt(2)

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca,|veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If vecc is as unit vector such that veca.vecb=veca.vecc=0 and theta= (pi/6) then veca= (A) +-1/2(vecbxxvecc) (B) +-(vecbxxvecc) (C) +-2(vecbxxvecc) (D) none of these

Consider three vectors veca, vecb and vecc . Vectors veca and vecb are unit vectors having an angle theta between them For vector veca,|veca|^2=veca.veca If veca_|_vecb and veca_|_vecc then veca||vecbxxvecc If veca||vecb, then veca=tvecb Now answer the following question: If |vecc|=4, theta cos^-1(1/4) and vecc-2vecb=tvecas, then t= (A) 3,-4 (B) -3,4 (C) 3,4 (D) -3,-4

If veca and vecb are unit vectors inclined at an angle theta , then the value of |veca-vecb| is

ARIHANT MATHS-PRODUCT OF VECTORS-Exercise (More Than One Correct Option Type Questions)
  1. Let vecr be a unit vector satisfying vecrxxveca=vecb, where |veca|=sqr...

    Text Solution

    |

  2. a1, a2, a3, in R-{0} and a1+a2cos2x+a3sin^2x=0fora l lx in R , then ...

    Text Solution

    |

  3. If veca and vecb are two vectors and angle between them is theta , the...

    Text Solution

    |

  4. If the unit vectors veca and vecb are inclined at an angle 2theta such...

    Text Solution

    |

  5. If vec a xx (vec bxxvec c)+(vec a*vec b)vec b=(4-2beta-sinalpha)vec b...

    Text Solution

    |

  6. If in triangle A B C , vec A B= vec u/(| vec u|)-- vec v/(| vec v|)a n...

    Text Solution

    |

  7. If a, b and c be the three non-zero vectors satisfying the condition a...

    Text Solution

    |

  8. Given the following informations about the non-zero vectors A, B and C...

    Text Solution

    |

  9. Let a, b and c are non-zero vectors such that they are not orthogonal ...

    Text Solution

    |

  10. Given three vectors U=2hat(i)+3hat(j)-6hat(k), V=6hat(i)+2hat(j)+2hat(...

    Text Solution

    |

  11. Let vec a=2 hat i- hat j+ hat k , vec b= hat i+2 hat j= hat ka n d ve...

    Text Solution

    |

  12. Three vectors veca,vecb,vecc are such that vecaxxvecb= 3(vecaxxvecc)Al...

    Text Solution

    |

  13. Let a, b and c be non-zero vectors and |a|=1 and r is a non-zero vecto...

    Text Solution

    |

  14. If veca and vecb are two unit vectors perpendicular to each other and...

    Text Solution

    |

  15. Given three non-coplanar vectors OA=a, OB=b, OC=c. Let S be the centre...

    Text Solution

    |

  16. If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j), then the vectors (a*hat...

    Text Solution

    |

  17. If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat ka n d...

    Text Solution

    |

  18. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

    Text Solution

    |

  19. Let the unit vectors a and b be perpendicular and the unit vector c be...

    Text Solution

    |

  20. If veca, vecb, vecc are three non-zero vectors, then which of the foll...

    Text Solution

    |