Home
Class 12
MATHS
Statement-I A=2hat(i)+3hat(j)+6hat(k), B...

Statement-I `A=2hat(i)+3hat(j)+6hat(k), B=hat(i)+hat(j)-2hat(k) and C=hat(i)+2hat(j)+hat(k)`, then `|Atimes(Atimes(AtimesB))*C|=243`
Statement-II `|Axx(Axx(AxxB))*C|=|A|^(2)|[A B C]|`

Promotional Banner

Topper's Solved these Questions

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

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If four points 2hat(i) + hat(j) + hat(k), hat(i) + hat(j) - hat(k), hat(j) - hat(k) and lamda hat(j) + hat(k) are coplanar then lamda =

The lines vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k)) and vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k)) are -

If the vectors ahat (i) + a hat (j) + c hat (k) , hat (i) + hat (k) and c hat (i) + c hat (j) + b hat (k) be coplanar, show that c^(2) = ab

Show that the vectors a = 2 hat (i) + 3hat (j) + 6 hat (k) , b = 3 hat (i) - 6 hat (j) + 2 hat (k) and c= 6 hat (i) + 2 hat (j) - 3 hat (k) are mutually perpendicular

If vec(a)=2hat(i)+3hat(j)-4hat(k) " and " vec(b)=hat(i)+2hat(j)+hat(k) , then find (vec(a)+vec(b)) " and " abs(vec(a)+vec(b)).

If vec(a)=2hat(i)-5hat(j)+3hat(k) " and " vec(b)=hat(i)-2hat(j)-4hat(k) , find the value of abs(3vec(a)+2vec(b)).

if vec a = 2 hat i- 3 hat j+hat k and vec b = hat i+2 hat j- 3hat k then vec aXvec b is

If vec a= 2 hat i- hat j+ hat k and vec b = - hat i+3 hat j+4 hat k ,then veca.vecb =

Show that the vectors are mutually perpendicular hat (i) + 2 hat (j) + hat (k) ,hat (i) + hat (j) - 3 hat (k) and 7 hat (i) - 4 hat (j) + hat (k)

Find the angle between the lines vec(r)=(3hat(i)+hat(j)-4hat(k))+t(hat(i)+hat(j)+hat(k)) and vec(r)=(5hat(i)-hat(j))+t'(3hat(i)+2hat(j)+4hat(k))

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. Let vec r be a non-zero vector satisfying vec r dot vec a= vec rdo...

    Text Solution

    |

  2. Let vec a=a1 hat i+a2 hat j+a3 hat k , vec b=b1 hat i+b2 hat j+b3 hat...

    Text Solution

    |

  3. Statement-I A=2hat(i)+3hat(j)+6hat(k), B=hat(i)+hat(j)-2hat(k) and C=h...

    Text Solution

    |

  4. If vec a , vec b ,a n d vec c are mutually perpendicular vectors a...

    Text Solution

    |

  5. Let vectors vec a , vec b , vec c ,a n d vec d be such that ( vec ax...

    Text Solution

    |

  6. The number of vectors of unit length perpendicular to vectors vec ...

    Text Solution

    |

  7. Prove that ( vec a.hat i)( vec axx hat i)+( vec a.j)( vec axx hat j)+(...

    Text Solution

    |

  8. Let vecf(t)=[t] hat i+(t-[t]) hat j+[t+1] hat k , w h e r e[dot] deno...

    Text Solution

    |

  9. If vec a is parallel to vec bxx vec c , then ( vec axx vec b).( vec ...

    Text Solution

    |

  10. The three vectors hat i+hat j,hat j+hat k, hat k+hat i taken two at a ...

    Text Solution

    |

  11. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vec...

    Text Solution

    |

  12. If |a|=2a n d|b|=3 and adotb=0,t h e n(axx(axx(axx(axxb)))) is equal t...

    Text Solution

    |

  13. If the two diagonals of one its faces are 6 hat i+6 hat ka n d4 hat ...

    Text Solution

    |

  14. The volume of a tetrahedron formed by the coterminous edges vec a ...

    Text Solution

    |

  15. If vec a , vec b , and vec c are three mutually orthogonal unit vector...

    Text Solution

    |

  16. Vector vec c is perpendicular to vectors vec a=(2,-3,1)a n d vec b...

    Text Solution

    |

  17. Given vec a=x hat i+y hat j+2 hat k , vec b= hat i- hat j+ hat k , ve...

    Text Solution

    |

  18. vec aa n d vec b are two unit vectors that are mutually perpendicu...

    Text Solution

    |

  19. If vec ra n d vec s are non-zero constant vectors and the scalar ...

    Text Solution

    |

  20. The scalar vec Adot [( ( vec B+ vec C)xx( vec A+ vec B+ vec C))] eq...

    Text Solution

    |