Home
Class 12
MATHS
Show that hat(i) xx (vec(a) xx hat(i)) +...

Show that `hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) + hat(k) xx (vec(a) xx hat(k)) = 2 vec(a)`.

Text Solution

Verified by Experts

The correct Answer is:
`2vec(a)`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    ARIHANT PRAKASHAN|Exercise TOPIC -2 (PRACTICE QUESTIONS) (6 MARK QUESTIONS) |12 Videos

  • VECTORS

    ARIHANT PRAKASHAN|Exercise TOPIC TEST 2|21 Videos

  • VECTORS

    ARIHANT PRAKASHAN|Exercise TOPIC -2 (PRACTICE QUESTIONS) (1 MARK QUESTIONS) |34 Videos

  • THREE DIMENSIONAL GEOMETRY

    ARIHANT PRAKASHAN|Exercise CHAPTER TEST|24 Videos

  • VERY SIMILAR TEST 1

    ARIHANT PRAKASHAN|Exercise Section C |10 Videos

Similar Questions

Explore conceptually related problems

Show that the vectors vec(a) = 3hat(i) - 2hat(j) + hat(k), vec(b) = hat(i) - 3hat(j) + 5hat(k) and vec(c) = 2hat(i) + hat(j) - 4hat(k) form a right angled triangle.

Show that the vectors vec(a) = hat(i) - 2hat(j) + 3hat(k), vec(b) = -2hat(i) + 3hat(j) - 4hat(k) and vec(c) = hat(i) - 3hat(j) + 5hat(k) are coplanar.

If vec(r) = x hat(i) + y hat(j) + z hat(k) , then find (vec(r) xx hat(i)).(vec(r) xx hat(j)) + xy .

For an vector vec(r) = x hat(i) + y hat(j) + z hat(k) , prove that vec(r) = (vec(r). hat(i))hat(i) + (vec(r).hat(j))hat(j) + (vec(r) .hat(k)) hat(k)

ARIHANT PRAKASHAN-VECTORS -TOPIC -2 (PRACTICE QUESTIONS) (4 MARK QUESTIONS)
  1. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

    Text Solution

    |

  2. Prove that for any three vectors vec(a), vec(b) and vec(c), [vec(a) + ...

    Text Solution

    |

  3. Show that hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) ...

    Text Solution

    |

  4. Find the area of the triangle ABC with vertices A(1,2,4), B(3,1,-2) an...

    Text Solution

    |

  5. If vec a, vec b, vec c are mutually perpendicular vectors of equal mag...

    Text Solution

    |

  6. Prove that [vec(a)xxvec(b)vec(b)xxvec(c )vec(c)xxvec(a)]=[vec(a)vec(b)...

    Text Solution

    |

  7. Prove that the following vectors can never be coplanar for any real va...

    Text Solution

    |

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

    Text Solution

    |

  9. If vec(a),vec(b) and vec(c ) are mutually perpendicular vectors, then ...

    Text Solution

    |

  10. Find a vector vec(b) such that vec(a) xx vec(b) = vec(c) and vec(a).ve...

    Text Solution

    |

  11. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

    Text Solution

    |

  12. The diagonals of a parallelogram are given by vec(a)=2hat(i)-3hat(j)+5...

    Text Solution

    |

  13. Resolve the vector vec(b) = hat(i) + hat(j) + hat(k) into vectors para...

    Text Solution

    |

  14. Prove that the following vectors are coplanar -4hat(i) + 4hat(j) + 4ha...

    Text Solution

    |

  15. If the magnitude of the difference of two unit vectors is sqrt3 then f...

    Text Solution

    |

  16. Find the value of t, such that the following vectors are perpendicular...

    Text Solution

    |

  17. Find the unit vector perpendicular to the vectors 2hat(i)-hat(j)+hat(k...

    Text Solution

    |

  18. Find |vec(a)|" and "|vec(b)|," if "(vec(a)+vec(b))*(vec(a)-vec(b))=8 a...

    Text Solution

    |

  19. If vec(a)xxvec(b)=vec(c)xxvec(d) and vec(a)xxvec(c)=vec(b)xxvec(d), th...

    Text Solution

    |

  20. If vec(a)=3hat(i)-2hat(j)-2hat(k) and vec(b)=2hat(i)+3hat(j)+hat(k), t...

    Text Solution

    |