Home
Class 12
MATHS
Prove that hat(i)times(a+hat(i))+hat(j)t...

Prove that `hat(i)times(a+hat(i))+hat(j)times(atimeshat(j))+hat(k)times(atimeshat(k))=2a`

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If u=hat(i)(atimeshat(i))+hat(j)(atimeshat(j))+hat(k)(atimeshat(k)) , then

The value of hat(i).(hat(j) xx hat(k))+ hat(j). (hat(i) xxhat(k)) + hat(k) . (hat(i) xx hat(j))

Prove that hat(i) xx hat(j) = hat(k) hat(i) xx hat(j) = 1xx 1 sin 90 hat(n) = hat(n)

If a=hat(i)+hat(j)+hat(k) and b=hat(i)-hat(j) , then the vectors (a*hat(i))hat(i)+(a*hat(j))hat(j)+(a*hat(k))hat(k), (b*hat(i))hat(i)+(b*hat(j))hat(j)+(b*hat(k))hat(k) and hat(i)+hat(j)-2hat(k)

Prove that lines vec( r)= (hat(i)+ hat(j) + hat(k))+ t(hat(i) - hat(j) + hat(k)) and vec(r ) = (3hat(i) - hat(k)) + s(4hat(j) - 16hat(k)) intersect. Also find the position vector of their point of intersection

The value of (hat(k) xx hat(j)). hat(i) + hat(j).hat(k) =

If a=hat(i)+2hat(j)-2hat(k), b=2hat(i)-hat(j)+hat(k) and c=hat(i)+3hat(j)-hat(k) , then atimes(btimesc) is equal to

Find the value of lamda , if the points with position vectors 3hat(i)- 2hat(j)- hat(k), 2hat(i) + 3hat(j)- 4hat(k), -hat(i) + hat(j) + 2hat(k), 4hat(i) + 5hat(j) + lamda hat(k) are coplanar.

Show that the vectors hat(i)-hat(j)-6hat(k),hat(i)-3hat(j)+4hat(k)and2hat(i)-5hat(j)+3hat(k) are coplanar.

The sum of the distinct real values of μ for which the vectors, muhat(i)+hat(j)+hat(k),hat(i)+muhat(j)+hat(k),hat(i)+hat(j)+muhat(k) are co-planar is :

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. If vec a , a n d vec b are unit vectors , then find the greatest v...

    Text Solution

    |

  2. Let G1, G2a n dG3 be the centroids of the triangular faces O B C ,O ...

    Text Solution

    |

  3. Prove that hat(i)times(a+hat(i))+hat(j)times(atimeshat(j))+hat(k)times...

    Text Solution

    |

  4. If hat ixx[( vec a- hat j)xx hat i]+ hat jxx[( vec a- hat k)xx hat j]...

    Text Solution

    |

  5. Let vec a , vec b ,and vec c be any three vectors, then prove that ...

    Text Solution

    |

  6. If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- ve...

    Text Solution

    |

  7. If vec a , vec b , vec c are mutually perpendicular unit vectors, fin...

    Text Solution

    |

  8. If a ,ba n dc are three non-cop0lanar vector, non-zero vectors then ...

    Text Solution

    |

  9. Prove that vectors vec u=(a l+a1l1) hat i+(a m+a1m1) hat j+(a n+a1n1)...

    Text Solution

    |

  10. For any four vectors, prove that ( veca × vecb )×( vecc × vec...

    Text Solution

    |

  11. If vec ba n d vec c are two-noncollinear vectors such that vec a...

    Text Solution

    |

  12. If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) ...

    Text Solution

    |

  13. Let vec a , vec ba n d vec c be pairwise mutually perpendicular v...

    Text Solution

    |

  14. Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a|...

    Text Solution

    |

  15. If |veca|=3, |vecb|=4 and the angle between veca and vecb is 120^(@) ....

    Text Solution

    |

  16. If vec a , vec b ,a n d vec c be three non-coplanar vector and p,q,...

    Text Solution

    |

  17. Find | -> a| and | -> b| , if ( -> a+ -> b)dot( -> a- -> b)=8 an...

    Text Solution

    |

  18. Let vec a , vec b ,a n d vec ca n d vec a^' , vec b^' , vec c ' are r...

    Text Solution

    |

  19. If vec a , vec b and vec c are three non-coplanar vectors, then ( v...

    Text Solution

    |

  20. Find the vector equation of the plane passing through the points havin...

    Text Solution

    |