Home
Class 12
MATHS
For an vector vec(r) = x hat(i) + y hat(...

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)`

Promotional Banner

Topper's Solved these Questions

  • TEST PAPER 10

    MODERN PUBLICATION|Exercise EXERCISE|33 Videos

  • TEST PAPER 3

    MODERN PUBLICATION|Exercise PROBLEM|63 Videos

Similar Questions

Explore conceptually related problems

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 .

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.

MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Answer the following: What is the value of [[o,-h,-g],[h,o,-f],[g,f,...

    Text Solution

    |

  2. Show that no two normals to a parabola are parallel.

    Text Solution

    |

  3. Find the intervals where the following functions are (a) increasing an...

    Text Solution

    |

  4. Find int (cos x /sin^(2) x + sin x ) dx

    Text Solution

    |

  5. Evaluate : int(0) ^(pi/4) dx/cos x (cos x + sin x).

    Text Solution

    |

  6. Find the differential equation whose general soltution is c1x^2+c2y=1 ...

    Text Solution

    |

  7. Find the area of the region bounded by the curve y=6x-x^(2), the X-axi...

    Text Solution

    |

  8. Prove the following by vector method. The parallelogram whose diagonal...

    Text Solution

    |

  9. Prove that the two lines whose direction cosines are connected by the ...

    Text Solution

    |

  10. A variable plane meets the coordinate axes at A, B, C and is at a cons...

    Text Solution

    |

  11. Find the equation of the line through the point (3, -1, 2) and paralle...

    Text Solution

    |

  12. If N denotes the set of all natural numbers and R be the relation on N...

    Text Solution

    |

  13. If a, b and c are all positive real, then prove that minimum value of ...

    Text Solution

    |

  14. Solve the following system of equations by the matrix inversion method...

    Text Solution

    |

  15. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

    Text Solution

    |

  16. Show that of all the rectangles inscribed in a given fixed circle, the...

    Text Solution

    |

  17. Evaluate : int dx /cosx (5+3 cos x).

    Text Solution

    |

  18. Find the area of the parallelogram whose diagonals are the vectors 3ha...

    Text Solution

    |

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

    Text Solution

    |

  20. Find the equation of plane through the point (2,0,-3) and containing t...

    Text Solution

    |